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The article focuses on a noninvasive method and system of quantifying postural stability of patients undergoing vestibular schwannoma microsurgery. Recent alternatives quantifying human postural stability are rather limited. The major drawback is that the posturography system can evaluate only two physical quantities of body movement and can be measured only on a transverse plane. A complex movement pattern can be, however, described more precisely while using three physical quantities of 3-D movement. This is the reason why an inertial measurement unit (Xsens MTx unit), through which we obtained 3-D data (three Euler angles or three orthogonal accelerations), was placed on the patient’s trunk. Having employed this novel method based on the volume of irregular polyhedron of 3-D body movement during quiet standing, it was possible to evaluate postural stability. To identify and evaluate pathological balance control of patients undergoing vestibular schwannoma microsurgery, it was necessary to calculate the volume polyhedron using the 3-D Leibniz method and to plot three variables against each other. For the needs of this study, measurements and statistical analysis were made on nine patients. The results obtained by the inertial measurement unit showed no evidence of improvement in postural stability shortly after surgery (4 days). The results were consistent with the results obtained by the posturography system. The evaluated translation variables (acceleration) and rotary variables (angles) measured by the inertial measurement unit correlate strongly with the results of the posturography system. The proposed method and application of the inertial measurement unit for the purpose of measuring patients with vestibular schwannoma appear to be suitable for medical practice. Moreover, the inertial measurement unit is portable and, when compared to other traditional posturography systems, economically affordable. Inertial measurement units can alternatively be implemented in mobile phones or watches.

Sensory nervous system disorders adversely affect postural stability of patients [

In clinical practice, stabilometric platforms are employed for the evaluation of patients’ postural stability. These platforms monitor the movement in the centre of pressure (CoP); subsequently, the motion is assessed by means of quantitative CoP indicators [

Stabilometric platforms do not allow for the study of individual body segments’ movement. Their other drawback is that they can monitor the movement of a body only in the transverse and not the other anatomical planes (frontal and sagittal). For these reasons, in patients with instability disorders, inertial measurement units (IMU) are increasingly being used for the accurate measurement of movement of specific body segments [

In clinical practice, the IMU commonly used for quantification of body segment movement are only for measurement and evaluation of one or two measured quantities, usually sway and angles [

The second objective, which, from a technical point of view, is equally important, is to propose and present a suitable method for quantitative assessment of the 3-D motion measured by IMU for postural stability in stance. Traditional methods used for quantitative assessments of postural stability in stance are usually based on the processing of two-dimensional (2-D) data from stabilometric platforms [

The selected assessment method of 2-D data will be adjusted to assess 3-D data, and the results obtained by this modified method will be compared with those obtained from the stabilometric platform. The reason for using a complete set of 3-D data, assessing postural stability of stance, is that using just two variables in 3-D motion may cause a loss of information about the third component of motion of a particular segment in space.

Using a quantitative assessment of the 3-D data, information on the overall movement of a particular body segment in the 3-D space can be obtained. For further research, a segment on a patient’s trunk was found as the most suitable to attach the IMU system. A similar application measuring angles of movement (MoCap) has been already successfully used in assessing postural stability in stance [

The final aim of this work, in terms of clinical application, is to demonstrate the difference in a patient’s stability while performing different stance tasks both pre- and postsurgery. The outcome of this test is to be a statement, whether there is any change in postural stability of patients shortly after the surgery [

Nine patients undergoing VS microsurgery were involved in the study. The surgery was performed in Motol University Hospital in the Department of Otolaryngology and Head and Neck Surgery of the 1st Faculty of Medicine, Charles University, in Prague. The subjects for measurement were randomly selected from the first half of 2014 to the first half of 2015. The patients, comprising of four men and five women averaging 46.7 (SD 11.9) years of age, were subjected to the measurement twice: before surgery and then 4 days after surgery.

Audiometric (pure-tone audiometry, speech audiometry, stapedial reflex, otoacoustic emissions, and brainstem auditory-evoked potentials) and neurootologic tests (clinical testing, electronystagmography, spontaneous nystagmus, gaze directional test, saccades, smooth pursuit, caloric test and head impulse and head shaking test, subjective visual vertical, and posturography) were taken along with magnetic resonance imaging in all the patients.

All nine patients were operated on by the same team of surgeons, using the retrosigmoid-transmeatal approach in the supine position. The surgeons used microsurgical endoscopy and techniques with intraoperative neuromonitoring. In all nine cases, the tumors were removed. The section of both vestibular parts of the 8th cranial nerve was performed even in the cases where continuity could be preserved.

The study was performed in accordance with the Declaration of Helsinki. The study protocol was approved by the local Ethical Committee of Motol University Hospital, and informed consent was obtained from all the subjects involved.

To measure trunk movements, specifically shift and sway, we used the Xbus Master (Xsens Technologies B.V.), a lightweight (330 g) and portable device using MTx units for orientation and acceleration measurement of body segments (see Figure

The MTx unit employed to measure angles and accelerations of the trunk and the Synapsys posturography system used to measure the CoP displacements.

The MTx unit was calibrated before each clinical examination. The MTx unit was set up in the following ways: one axis of the MTx’s coordinate system was parallel to the anterior-posterior axis, that is, the symmetry axis of the fixed stationary platform of the Synapsys posturography system, on which the participants stood. The other two axes were perpendicular to the anterior-posterior axis (i.e., the symmetry axis of the platform) respecting the Earth’s gravitational direction, that is, the superior-inferior axis was colinear with the direction of gravity. After calibration, the MTx unit was placed on the patient’s trunk according to [

The data, that is, the three Euler angles (roll (

The data, obtained from the IMU, were compared with the data obtained by the traditional method based on CoP measurement. The values of centre of pressure (CoP) displacement (i.e., postural sway) were measured by a posturography system, the Synapsys posturography system (Synapsys Inc.).

Body sway was measured by the Xsens system and Synapsys posturography system during a still stance on a firm surface (FiS) and a soft foam surface (FoS) with eyes open (EO) and eyes closed (EC) [

The three Euler angles and three accelerations in the accelerometer coordinate system were used to calculate the accelerations in the global reference system and then in the anatomical coordinate frame. The calculation was based on the rotational matrices. The rotation matrices rotate an acceleration vector

The novel method for identification of pathologies affecting balance control is based on the mathematical tools for static posturography [

In more detail, the original Leibniz method proposes an evaluation of stability by calculating the area bounded by the 2-D data points located in predefined zones relative to the median of the 2-D data. The 2-D data, which is obtained from a measurement system, is able to register the variation of

Polygon area calculation via the 2-D Leibniz method and by plotting mediolateral (ML) and anterior-posterior (AP) accelerations versus each other.

Such a method can be modified for stability evaluation by calculating the volume bounded by the 3-D data points located in the predefined zones relative to the median of 3-D data (

Divide spherical space into subsets of the points obtained by plotting superior-inferior (SI), mediolateral (ML), and anterior-posterior (AP) accelerations versus each other.

Algorithm for calculation of the total volume of 3-D polyhedron.

(1) Calculate the median of the distribution of |

(2) Set the origin of the frame of reference to the median of the distribution. |

(3) Convert the Cartesian coordinates of each data point |

(4) Divide the data into subsets belonging to sectors of the 3-D space predefined by |

(5) In each subset |

(6) Calculate the volume of each pyramid with one vertex at the origin of the reference frame and four vertices at the points |

(7) Calculate the total volume of 3-D polyhedron (see Figure |

The method used to calculate the volume of each elemental pyramid is based on a calculation of the convex polyhedron volume [_{max} among all points in four subsets belonging to four adjacent sectors (see Figure

Volume polyhedron calculation by the 3-D Leibniz method and plotting superior-inferior (SI), mediolateral (ML), and anterior-posterior (AP) accelerations versus each other.

For a convex polyhedron computation in MatLab, Delaunay triangulation [^{3}·s^{−6} or deg^{3}. It is also necessary to mention that the MTx unit also records gravitational acceleration which does not have to be subtracted. The calculation of the polyhedron volume exploits only changes in the accelerations, and the gravitational acceleration is constant and perpendicular to the horizontal plane of the Earth’s surface. In spite of this, gravitational acceleration was also subtracted in the MatLab software. To compare the data obtained by the posturography system with data obtained by the IMU, the area of the 95% confidence ellipse (ACE) and 2-dimensional path length (PL) of CoP excursions was used. The Synapsys posturography system directly calculated the areas and lengths, so the measured data did not have to be converted. The physical unit of the area is one mm^{2} whereas that of the length is one mm [

An example of a polyhedron obtained by plotting superior-inferior (SI), mediolateral (ML), and anterior-posterior (AP) accelerations versus each other.

After calculating the TVP, ACE, and PL of each patient pre- and postsurgery (while standing on a FiS and FoS with EO and EC), the Jarque–Bera test was used to identify a normal distribution of calculated characteristics [

The statistical data illustrate the differences in stance trials pre- and postsurgery (Tables

Comparison of the total volumes of the accelerated polyhedrons in patients pre- and postsurgery.

Presurgery | Postsurgery | ||||
---|---|---|---|---|---|

EO | EC | EO | EC | ||

FiS | Min (m^{3}·s^{−6}) |
4.58·10^{−4} |
4.75·10^{−4} |
2.57·10^{−4} |
7.63·10^{−4} |

Q1 (m^{3}·s^{−6}) |
5.16·10^{−4} |
8.59·10^{−4} |
7.02·10^{−4} |
1.87·10^{−3} | |

Mdn (m^{3}·s^{−6}) |
7.11·10^{−4} |
9.67·10^{−4} |
1.12·10^{−3} |
2.42·10^{−3} | |

Q3 (m^{3}·s^{−6}) |
1.06·10^{−3} |
9.26·10^{−3} |
1.80·10^{−3} |
6.45·10^{−3} | |

Max (m^{3}·s^{−6}) |
3.21·10^{−3} |
2.35·10^{−2} |
1.57·10^{−2} |
2.63·10^{−2} | |

FoS | Min (m^{3}·s^{−6}) |
2.31·10^{−3} |
4.70·10^{−2} |
2.31·10^{−3} |
2.73·10^{−2} |

Q1 (m^{3}·s^{−6}) |
4.22·10^{−3} |
5.48·10^{−2} |
5.89·10^{−3} |
2.06·10^{−1} | |

Mdn (m^{3}·s^{−6}) |
1.04·10^{−2} |
1.45·10^{−1} |
7.00·10^{−3} |
5.78·10^{−1} | |

Q3 (m^{3}·s^{−6}) |
1.18·10^{−2} |
5.22·10^{−1} |
3.67·10^{−2} |
1.24·10^{+0} | |

Max (m^{3}·s^{−6}) |
3.25·10^{−2} |
2.40·10^{+0} |
4.49·10^{−2} |
8.95·10^{+0} |

EO: eyes open; EC: eyes closed; FiS: firm surface; FoS: foam surface; Min: minimum; Max: maximum; Mdn: median; Q1: first quartile; Q3: third quartile.

Comparison of the total volumes of the polyhedrons of angles in patients pre- and postsurgery.

Presurgery | Postsurgery | ||||
---|---|---|---|---|---|

EO | EC | EO | EC | ||

FiS | Min (deg^{3}) |
4.62·10^{−2} |
5.68·10^{−2} |
3.73·10^{−2} |
5.97·10^{−2} |

Q1 (deg^{3}) |
9.12·10^{−2} |
1.30·10^{−1} |
7.62·10^{−2} |
2.61·10^{−1} | |

Mdn (deg^{3}) |
1.26·10^{−1} |
1.64·10^{−1} |
3.71·10^{−1} |
6.98·10^{−1} | |

Q3 (deg^{3}) |
2.18·10^{−1} |
9.26·10^{−1} |
7.99·10^{−1} |
3.60·10^{+0} | |

Max (deg^{3}) |
3.85·10^{+0} |
1.47·10^{+1} |
4.94·10^{+0} |
8.35·10^{+0} | |

FoS | Min (deg^{3}) |
2.74·10^{−1} |
7.96·10^{−1} |
2.33·10^{−1} |
1.53·10^{+0} |

Q1 (deg^{3}) |
3.42·10^{−1} |
1.21·10^{+0} |
2.73·10^{−1} |
7.61·10^{+0} | |

Mdn (deg^{3}) |
8.81·10^{−1} |
1.28·10^{+1} |
6.75·10^{−1} |
4.32·10^{+1} | |

Q3 (deg^{3}) |
1.68·10^{+0} |
1.83·10^{+1} |
3.28·10^{+0} |
7.41·10^{+1} | |

Max (deg^{3}) |
8.24·10^{+0} |
7.98·10^{+1} |
1.18·10^{+2} |
7.00·10^{+2} |

EO: eyes open; EC: eyes closed; FiS: firm surface; FoS: foam surface; Min: minimum; Max: maximum; Mdn: median; Q1: first quartile; Q3: third quartile.

Comparison of the areas of the 95% confidence ellipses in patients pre- and postsurgery.

Presurgery | Postsurgery | ||||
---|---|---|---|---|---|

EO | EC | EO | EC | ||

FiS | Min (mm^{2}) |
1.21·10^{+2} |
4.90·10^{+1} |
7.30·10^{+1} |
1.22·10^{+2} |

Q1 (mm^{2}) |
1.74·10^{+2} |
1.88·10^{+2} |
1.48·10^{+2} |
4.45·10^{+2} | |

Mdn (mm^{2}) |
1.89·10^{+2} |
6.34·10^{+2} |
4.15·10^{+2} |
8.05·10^{+2} | |

Q3 (mm^{2}) |
4.66·10^{+2} |
1.04·10^{+3} |
6.60·10^{+2} |
1.10·10^{+3} | |

Max (mm^{2}) |
5.64·10^{+3} |
9.06·10^{+3} |
1.13·10^{+3} |
3.20·10^{+3} | |

FoS | Min (mm^{2}) |
2.54·10^{+2} |
7.62·10^{+2} |
4.14·10^{+2} |
1.40·10^{+3} |

Q1 (mm^{2}) |
5.05·10^{+2} |
1.08·10^{+3} |
5.49·10^{+2} |
4.79·10^{+3} | |

Mdn (mm^{2}) |
8.16·10^{+2} |
6.17·10^{+3} |
1.23·10^{+3} |
7.47·10^{+3} | |

Q3 (mm^{2}) |
1.59·10^{+3} |
8.49·10^{+3} |
1.60·10^{+3} |
1.16·10^{+4} | |

Max (mm^{2}) |
6.08·10^{+3} |
1.34·10^{+4} |
8.66·10^{+3} |
1.81·10^{+4} |

EO: eyes open; EC: eyes closed; FiS: firm surface; FoS: foam surface; Min: minimum; Max: maximum; Mdn: median; Q1: first quartile; Q3: third quartile.

Comparison of the path lengths of CoP excursions in patients pre- and postsurgery.

Presurgery | Postsurgery | ||||
---|---|---|---|---|---|

EO | EC | EO | EC | ||

FiS | Min (mm) | 2.51·10^{+2} |
2.87·10^{+2} |
2.94·10^{+2} |
3.62·10^{+2} |

Q1 (mm) | 2.82·10^{+2} |
4.16·10^{+2} |
3.34·10^{+2} |
7.42·10^{+2} | |

Mdn (mm) | 3.45·10^{+2} |
4.83·10^{+2} |
5.18·10^{+2} |
8.19·10^{+2} | |

Q3 (mm) | 6.26·10^{+2} |
1.75·10^{+3} |
6.74·10^{+2} |
1.28·10^{+3} | |

Max (mm) | 9.65·10^{+2} |
1.86·10^{+3} |
2.26·10^{+3} |
3.17·10^{+3} | |

FoS | Min (mm) | 5.44·10^{+2} |
1.61·10^{+3} |
3.62·10^{+2} |
1.94·10^{+3} |

Q1 (mm) | 6.62·10^{+2} |
1.82·10^{+3} |
7.42·10^{+2} |
2.96·10^{+3} | |

Mdn (mm) | 1.00·10^{+3} |
3.63·10^{+3} |
8.19·10^{+2} |
4.17·10^{+3} | |

Q3 (mm) | 1.45·10^{+3} |
4.33·10^{+3} |
1.28·10^{+3} |
4.44·10^{+3} | |

Max (mm) | 2.05·10^{+3} |
5.35·10^{+3} |
3.17·10^{+3} |
6.94·10^{+3} |

Comparison of the data measured by IMU; TVPA: total volume of the polyhedron of the accelerations; TVPD: total volume of polyhedron of the angles; EO: eyes open; EC: eyes closed; FiS: firm surface; FoS: foam surface; B: presurgery; A: postsurgery.

Comparison of the data measured by posturography system; ACE: area of the confidence ellipse; PL: path length of CoP; EO: eyes open; EC: eyes closed; FiS: firm surface; FoS: foam surface; B: presurgery; A: postsurgery.

In almost all the cases, statistically significant differences were found in the data comparing stance trials (see Table

The calculated

Presurgery | Postsurgery | ||
---|---|---|---|

TVPA | EO FiS versus EO FoS | <0.01 |
<0.01 |

EC FiS versus EC FoS | <0.01 |
<0.01 | |

EO FiS versus EC FiS | 0.05 |
<0.01 | |

EO FoS versus EC FoS | <0.01 |
<0.01 | |

TVPD | EO FiS versus EO FoS | <0.01 |
0.07 |

EC FiS versus EC FoS | <0.01 |
<0.01 | |

EO FiS versus EC FiS | 0.12 | <0.01 | |

EO FoS versus EC FoS | <0.01 |
<0.01 | |

ACE | EO FiS versus EO FoS | <0.01 |
<0.01 |

EC FiS versus EC FoS | <0.01 |
<0.01 | |

EO FiS versus EC FiS | 0.07 | 0.03 | |

EO FoS versus EC FoS | <0.01 |
<0.01 | |

PL | EO FiS versus EO FoS | <0.01 |
<0.01 |

EC FiS versus EC FoS | <0.01 |
<0.01 | |

EO FiS versus EC FiS | <0.01 |
<0.01 | |

EO FoS versus EC FoS | <0.01 |
<0.01 |

TVPA: total volume of the polyhedron of accelerations; TVPD: total volume of the polyhedron of angles; ACE: area of the confidence ellipse; PL: path length of CoP; EO: eyes open; EC: eyes closed; FiS: firm surface; FoS: foam surface;

In the case of patients with EO standing on the FiS and FoS, the Spearman’s rank correlation coefficient indicates significant correlation between the TVPA or TVPD and ACE or PL. In the both cases, that is, pre- and postmicrosurgery, the correlations are moderate or slightly higher. In most cases, the patient examinations show strong or very strong positive correlations between the data measured by IMU and that measured by the posturographic platform (see Tables

Spearman’s rank correlation coefficient between the volume of polyhedron and the area of the confidence ellipse of CoP excursions.

Presurgery | Postsurgery | |||
---|---|---|---|---|

TVPA | TVPD | TVPA | TVPD | |

EO FiS | 0.65 |
0.57 |
0.70 |
0.87 |

EO FoS | 0.63 |
0.85 |
0.85 |
0.87 |

EC FiS | 0.77 |
0.80 |
0.62 |
0.75 |

EC FoS | 0.68 |
0.90 |
0.82 |
0.90 |

TVPA: total volume of the polyhedron of accelerations; TVPD: total volume of the polyhedron of angles; FiS: firm surface; FoS: foam surface; EO: eyes open; EC: eyes closed;

Spearman’s rank correlation coefficient between the volume of polyhedron and the path length of CoP excursions.

Presurgery | Postsurgery | |||
---|---|---|---|---|

TVPA | TVPD | TVPA | TVPD | |

EO FiS | 0.90 |
0.67 |
0.78 |
0.92 |

EO FoS | 0.82 |
0.97 |
0.51 |
0.60 |

EC FiS | 0.91 |
0.90 |
0.53 |
0.73 |

EC FoS | 0.95 |
0.87 |
0.90 |
0.72 |

TVPA: total volume of the polyhedron of accelerations; TVPD: total volume of the polyhedron of angles; FiS: firm surface; FoS: foam surface; EO: eyes open; EC: eyes closed;

No significant differences were found when comparing Pts pre- and postmicrosurgery with EO standing on FiS or FoS. A significant difference was observed only when comparing Pts pre- and postmicrosurgery with EC standing on FoS. A significant difference was observed by TVPD and PL, (see Table

The calculated

TVPA | EO-FiS | 0.13 |

EO-FoS | 0.50 | |

EC-FiS | 0.91 | |

EC-FoS | 0.10 | |

TVPD | EO-FiS | 0.30 |

EO-FoS | 0.91 | |

EC-FiS | 0.50 | |

EC-FoS | 0.02^{∗} | |

ACE | EO-FiS | 0.43 |

EO-FoS | 0.50 | |

EC-FiS | 0.50 | |

EC-FoS | 0.10 | |

PL | EO-FiS | 0.10 |

EO-FoS | 0.65 | |

EC-FiS | 0.65 | |

EC-FoS | 0.02 |

TVPA: total volume of polyhedron of the accelerations; TVPD: total volume of the polyhedron of angles; ACE: area of the confidence ellipse; PL: path length of CoP; FiS: firm surface; FoS: foam surface; EO: eyes open; EC: eyes closed;

The median of the TVPD in Pts postmicrosurgery is 3.4 times higher than the median of the TVPD in Pts presurgery. The median of the PL in Pts postsurgery is 1.2 times higher than the median of the PL in Pts presurgery. In all cases, the comparison of data showed that the effect sizes were moderate to large, that is, calculated values were higher than 0.4.

The aim of the study was to demonstrate the applicability of an IMU for assessing postural stability of patients with VS. In almost all cases, changes in stance conditions, that is, EO versus EC and FiS versus FoS, resulted in a statistically significant change of TVPA, TVPD, ACE, and PL values.

This study concludes that complicated stance tasks performed when either a mechanoreceptor or visual perception is reduced have a significant impact on trunk movements. The findings are consistent with those obtained when healthy subjects standing with EC were measured on FoS [

It was also found that there was a strong correlation between the recorded results from the posturography system achieved by the quantitative methods and those from the IMU. In most cases, they carried strong positive correlation characters. Conversely, no significant difference in terms of correlation was found between the results achieved by the TVPA method and those by TVPD with ACE and PL. Both methods correlate with ACE and PL similarly, data obtained by evaluation of accelerations, that is, from translational 3-D motion, reach the same conclusions as the data obtained by angle evaluation, that is, angular 3-D motion. The reason is that the large movements of the trunk, which improves the stability of the patient’s body, have a great impact on changing the centre of mass (CoM) of the whole body which corresponds to the position of the CoP [

The reason for the deterioration above may be that patient measurements were performed shortly after surgery, when they still did not undergo complete postoperative recovery. When measuring of postural stability was performed 8 days postsurgery (see [

Based on the results, it can be said that the position CoP of the whole body, which is traditionally subjected to assessments in patients with VS, is significantly affected by the position of their trunk. The results also show that in clinical practice, it is more suitable to perform the examination of subjects in a standing position with the EC placed on FoS since the postural control deficits can be identified more accurately.

As we have mentioned above, the measurement methodology is commonly used to measure postural stability by means of stabilometric platforms in clinical practice. Validation of the application of the inertial measurement unit was performed by comparative measurement using the stabilometric platform (see Tables

Nevertheless, there are some limitations to this research study. The most important is that the sample size of the subjects was too small and may not have been representative enough of the larger population. However, nine patients proved to be sufficient for the preliminary research which managed to test the basic attributes of the method proposed for further studies of postural stability. The size of the sample group can be compared to one used in similar research focused on studying the vestibular system [

It was also deemed unnecessary to compare patients of different ages, since the results demonstrate that the parameters of body sway of healthy subjects within the age range of 20 to 60 years vary only insignificantly [

The research conducted and this follow-up study on postural instability in patients with VS using an IMU placed on the patient’s trunk and the Leibniz method show that the method presented is suitable for the identification of postural balance problems. This technique described allows for the study of three measured variables (three angles and three accelerations) of 3-D body movement [

Reviewing the clinical findings, the measurement results are in line with the results of previous studies used for evaluation of stability on platforms. Although the postural stability of patients did not improve four days post operation, it is expected to improve after a complete recovery. It is therefore essential for new or subsequent research of patients with VS to focus on IMU testing in postural stability assessment over the long-term course of the recovery process.

The authors declare that they have no conflicts of interest.

This work was completed in Prague in the framework of research project SGS16/109/OHK4/1T/17 of CTU in Prague. The authors would like to thank Motol University Hospital for their collaborative research focusing on the development of methods and systems for evaluating the health conditions of patients.