Selection of Kinematic and Temporal Input Parameters to Define a Novel Upper Body Index Indicator for the Evaluation of Upper Limb Pathology

Abstract

Purpose: This work aimed to develop a novel indicator of upper limb manipulative movements. A principal component analysis (PCA) algorithm was applied to kinematic measurements of movements of the upper limbs performed during an everyday activity. Methods: Kinematics of the upper limb while drinking from a mug were investigated using the commercially available Xsens MVN BIOMECH inertial sensor-based motion capture system. The study group consisted of 20 male patients who had previously suffered an ischaemic stroke, whilst the reference group consisted of 16 males with no disorders of their motor organs. Based on kinematic data obtained, a set of 30 temporal and kinematic parameters were defined. From this, 16 parameters were selected for the determination of a novel indicator, the Upper Body Index (UBI), which served the purpose of assessing manipulative movements of upper limbs. Selection of the 16 parameters considered the percentage distribution of the parameters beyond the standard, the differences in mean values between the reference group and the study group, and parameter variability. Results: Analysis of kinematics allowed for the identification and selection of the parameters used in the development of the new index. This included 2 temporal parameters and 14 kinematic parameters, with the minimum and maximum angles of the upper limb joints, motion ranges in the joints, and parameters connected with movement of the spine recorded. These parameters were used to assess motion in the shoulder and elbow joints, in all possible planes, as well as spine movement. The values of the UBI indicator were as follows: in the case of the reference group: 13.67 ± 2.40 for the dominant limb, 13.71 ± 3.36 for the non-dominant limb; in the case of the stroke patient group: 130.86 ± 75.07 for the dominant limb, 155.58 ± 170.76 for the non-dominant limb. Conclusions: The developed UBI made it possible to discover deviations from the standard performance of upper limb movements. Therefore, the index may be applicable to the analysis of any sequence of movements carried out by the upper limb.

1. Introduction

Being able to properly perform daily activities is very important for the normal functioning of human beings. Indeed, correct functioning of the upper limbs has an impact on both physical and mental well-being. Evaluation of movements of the upper limbs is most frequently achieved by assessing motion kinematics.

Previous research into upper limb movement has focused on analysing ranges of motion [1,2,3,4,5] and performance during everyday activities, such as drinking from a mug [6,7,8,9,10,11] drinking from a glass, pouring from a kettle, turning a handle, lifting a bag to a shelf, turning a key [7], cup and box reach, as well as grasp and transfer [12], among others [13,14,15,16].

Current evaluation methods of upper limb functioning focus on obtaining quantitative data, which allows for the objective assessment of the degree of deviation of certain movements from a reference. It is assumed that the application of such objective methods contributes to a better and more precise understanding of movement patterns among healthy individuals and those with motor deficits.

The most common clinical method used to assess upper limb movement pathology is observation. Unfortunately, this method is subjective and depends on the experience of the person performing the test. The clinician’s inexperience may also cause him or her to subconsciously look for preconceived deviations from the norm. Although there are scales for functional assessment of the upper limbs related to observation, these scales are subjective. Their outcome depends directly on the person responsible for performing the test. Simultaneous observation of all body segments can also be a difficulty.

Three-dimensional motion analysis is frequently applied to the evaluation of upper limb movements, however, such analysis of complex kinematic courses is challenging and time-consuming for clinicians. Furthermore, it is often difficult to determine unequivocally from the above variables whether there has been an improvement or worsening of the upper limb movement stereotype. Some parameters may improve, while others may move away from the accepted movement norm. For this reason, indicators of movement evaluation are attracting greater interest. Such indicators enable assessment by means of just one non-dimensional value, which can be compared to data obtained from a reference group. Indicators of movement are also meaningful in assessing treatment progress. Treatment progress can be quantified and is not subjective/dependent on the clinician.

Indicator methods are mainly based on the application of statistical methods to identify mutual dependences between data, such as kinematic and spatio-temporal parameters.

The use of indicators in the assessment of upper limb functions is an effective method of supporting kinematic analysis [17,18]. However, there have only been a small number of studies carried out on the use of indicators for the assessment of the upper limbs [15,17,18,19,20,21,22].

Recent studies have devised a number of indexes for the upper limbs, such as the Arm Profile Score (APS) [15,19,20,21], the Pediatric Upper Limb Motion Index (PULMI) [17] and the Global Upper Limb Deviation Index (GULDI) [22,23]. The introduction of these indexes has allowed researchers to circumvent the analysis of large amounts of kinematic data, accelerating the evaluation of motor dysfunctions. Furthermore, an important asset of the use of indicators is the simplicity by which the data can be interpreted.

The APS is calculated on the basis of the difference in the root mean square (RMS) between kinematic parameters of a person with upper limb motor deficits and the mean values of healthy individuals [15]. This index considers 13 parameters that define the kinematics of the trunk, shoulder blade, shoulder joint, elbow joint and wrist. The APS may be broken down into 13 variables, these so-called Arm Variable Scores (AVS) represent the deviation of particular movement parameters of a given person from mean standard values [15].

The PULMI [17], UMDI [18] and GULDI indexes are based on an algorithm that calculates the Gait Deviation Index (GDI) proposed by Schwartz and Rozumalski [24]. Similar to the APS, these three indexes were built on the basis of the difference in the RMS between a set of kinematic parameters of test subjects and the mean values of the parameters recorded from healthy individuals.

A different mathematical algorithm, based on the distribution of chief components of PCA, was used in the development of the Gillette Gait Index (GGI), which is commonly applied to gait assessment [25]. Its computations are based on 16 kinematic and spatio-temporal parameters, obtained from the quantitative evaluation of gait, and is mainly used for assessment of gait functions in patients with infant cerebral palsy [25,26,27,28]. It appears that the mathematical algorithm of the GGI may also be applied to the assessment of motion pathology of the upper limbs. The most crucial element in the development of the new index based on the GGI algorithm is the selection of input parameters.

This work aimed to develop a methodology for assessing upper limb manipulative function from kinematic data of activities of daily living using the PCA algorithm. The study presents methods for selecting parameters that build the index. Implementation of this objective required the following:

• Collection of kinematic values differentiating between correct and pathological movements;
• Selection of a set of input parameters for the new index.
• Determination of the UBI for the reference group and patients with upper limb dysfunction caused by ischaemic stroke.

2. Materials and Methods

Figure 1 shows a flowchart illustrating the successive steps to develop a methodology for assessing upper limb manipulative function from kinematic data of activities of daily living using the PCA algorithm. The individual steps are discussed in detail in the sections below.

2.1. Participants

The reference group consisted of 16 male participants ranging from 19 to 29 years of age (age: 23 ± 2, body weight: 73.75 ± 8.57 kg, height 1.80 ± 0.07 m). All of the participants in the reference group indicated that their right upper limb was dominant. The inclusion criteria for acceptance were that they were healthy individuals with the absence of chronic disease, had no history of surgical procedures to their upper limbs or spine, and no injuries to the upper limbs in the preceding 6 months.

The second group consisted of 20 male patients ranging in age from 57 to 74 years (age: 63 ± 5, body weight: 79.90 ± 13.72 kg, height 1.70 ± 0.05 m) who had previously suffered an ischaemic stroke. All individuals identified their right limb as dominant. All of the stroke patients suffered from hemiparesis, 18 on the left-hand side and 2 on the right-hand side. For inclusion in this group, patients had to have paresis of one of their upper limbs due to an ischaemic stroke that had occurred in the previous 3 to 6 months. The patients were assessed for inclusion by physicians at the Miners’ Rehabilitation Centre “REPTY”, from the second week of their stay in hospital. Whilst admitted to the hospital, all patients were subjected to standard rehabilitation procedures. The exclusion criteria for stroke patients was the inability to drink from a mug, as this activity was the subject of the analysis. Motor ability of the patients was evaluated by physicians using tests and medical scales. Brunnstrom scale was used for the assessment of hand ability, whilst Ashworth’s scale was used for the evaluation of muscle tone and the degree of spasticity, and the Barthel scale was used to assess their performance in everyday activities. All of the participants obtained results within the range of 5–6 in the Brunnstorm scale, 0–2 in the Ashworth’s scale and 13–20 in the Barthel scale.

All participants were informed of the purpose and course of the tests and expressed their conscious consent to participate in the study.

This study was approved by the ethical committee of the Jerzy Kukuczka Academy of Physical Education in Katowice, Poland (protocol number 11/2015).

2.2. Experimental Testing

Movement kinematics were measured using the MVN BIOMECH inertial sensor-based motion capture system (Xsens Technologies B.V., Enskode, The Netherlands), which is equipped with 11 inertial sensors, set at a sampling frequency of 120 Hz. Sensors were placed on the head, sternum, sacral bone, and symmetrically on both upper limbs, to include the shoulder blades, arms, forearms and palms. Initial experiments involved the collection of anthropometric measurements and calibration of the system. Following this, kinematic measurements were recorded as participants drank from a mug. Each participant was assessed whilst sitting on a standard chair, with a seat height of 45 cm, at a table, which was 80 cm high. The starting position of the mug was clearly marked on the table surface and participants’ were tasked to drink from the mug naturally, without prior instruction. The only requirement was that the mug had to be returned to its marked starting position. The whole movement was divided into 3 phases, the lifting phase, the drinking phase, and the lowering phase, when the mug was returned to its starting position. Each participant performed the task of drinking from the mug three times. The subjects performed the activity with both hands. First with the dominant hand, then with the non-dominant hand.

This experiment allowed for the determination of the course of the kinematics of motion in the upper limb joints and the arrangement of particular segments of the spine. The kinematic motion waveforms of each repetition performed with the dominant and non-dominant hand were the basis for determining 30 input parameters (30 temporal and kinematic motion parameters identified in consultation with clinicians—see Section 2.4 for details). The 30 defined parameters (as single numerical values) were determined separately for each repetition of each subject, for both the dominant and non-dominant upper limb. The parameter results obtained for 3 repetitions (for each limb of the test subject) were not averaged. All values obtained for the tested subjects were included in the results database. The results database collected therefore included the values of the 30 parameters obtained for all repetitions performed with the dominant and non-dominant limb, for all healthy subjects (reference group) and patients. The results database therefore included 216 results for each defined parameter from P1 to P30. In total, the results database included 6480 values (36 subjects × 2 upper limbs × 3 repetitions × 30 parameters). This database was then used in calculations to select the parameters of the 3 defined criteria (M1, M2, M3). The UBI value was then determined for all 3 repetitions performed with the subject’s dominant and non-dominant limb. The evaluated value of the UBI index for the tested person is the average value of these 3 values obtained for subsequent repetitions.

2.3. Mathematical Algorithm of the Indicator

The UBI indicator was based on a PCA mathematical algorithm, which made it possible to obtain 16 independent variables from 16 selected motion variables [25]. The obtained sets of parameters were shown in the form of vectors in multidimensional space.

Development of the mathematical algorithm of the indicator consisted of two stages. The first stage involved the collection and standardisation of data from the reference group. A covariance matrix, eigenvectors and eigenvalues of the matrix were then calculated for these data. The second stage involved the collection and standardisation of data from stroke patients. Following that, the vector of coordinates of standardised points was determined, which represented the patients in a new system of coordinates. The final stage was the measurement of the Euclidean distance, showing to what degree the movement of stroke patients diverged from the mean calculated from the reference group.

The mathematical algorithm of the indicator was then implemented in the MatLab environment (Mathworks, Natick, MA, USA).

2.4. Selection of Input Parameters

The first phase focused on the selection of 30 kinematic parameters, which provided the basis for choosing the 16 parameters of the UBI indicator. Taking into consideration the mathematical algorithm, it was assumed that the parameters had to be presented in the form of a single numerical value. Thirty parameters were selected following consultations with physiotherapists and physicians at the Miners’ Rehabilitation Centre GCR ”REPTY”, as well as on the basis of the authors’ experience. The shortlisted parameters were selected from kinematic data collected during the analysed activity of drinking from a mug.

The following kinematic and temporal parameters were selected for the analysed activity:

• P1—Duration of the lifting phase t1 [s]—time from the moment of gripping the mug to the beginning of the drinking phase, which was defined as the lips touching the mug;
• P2—Duration of the lowering phase t2 [s]—time from the moment of the beginning of the movement after the drinking phase to the moment of placing the mug back onto its starting position;
• P3—Minimum flexion/extension angle of the shoulder joint;
• P4—Maximum flexion/extension angle of the shoulder joint;
• P5—Minimum abduction/adduction angle of the shoulder joint;
• P6—Maximum abduction/adduction angle of the shoulder joint;
• P7—Minimum external/internal rotation angle of the shoulder joint;
• P8—Maximum external/internal rotation angle of the shoulder joint;
• P9—Minimum flexion/extension angle of the elbow joint;
• P10—Maximum flexion/extension angle of the elbow joint;
• P11—Minimum supination/pronation angle of the elbow joint;
• P12—Maximum supination/pronation angle of the elbow joint;
• P13—Minimum palmar flexion/dorsiflexion angle of the wrist joint;
• P14—Maximum palmar flexion/dorsiflexion angle of the wrist joint;
• P15—Minimum elbow/radial abduction angle of the wrist joint;
• P16—Maximum elbow/radial abduction angle of the wrist joint;
• P17—Minimum spine anteversion angle;
• P18—Maximum spine anteversion angle;
• P19—Minimum spine rotation angle;
• P20—Maximum spine rotation angle;
• P21—Minimum spine anteversion angle in section Th1-Th12;
• P22—Maximum spine anteversion angle in section Th1-Th12;
• P23—Minimum spine rotation angle in section Th1-Th12;
• P24—Maximum spine rotation angle in section Th1-Th12;
• P25—Minimum spine anteversion angle in section L1-L5;
• P26—Maximum spine anteversion angle in section L1-L5;
• P27—Minimum spine rotation angle in section L1-L5;
• P28—Maximum spine rotation angle in section L1-L5;
• P29—Abduction/adduction motion range of the shoulder joint;
• P30—External/internal rotation motion range of the shoulder joint.

The next phase involved surveying of physicians and physiotherapists in order to understand their experience of examining motor functions in the upper limbs of patients after stroke. In the survey, these healthcare professionals indicated their specialisation and provided answers related to their experience in the treatment/rehabilitation of patients after ischaemic stroke, gave an estimation of the number of treated/rehabilitated patients after ischaemic stroke, and the level of their knowledge in the application of biomechanical systems to the rehabilitation of patients after ischaemic stroke. In order to aid in the selection of parameters for the development of the new indicator, they were asked: “In your opinion, which parameters have the highest diagnostic value in the assessment of motor functions of the upper limbs in patients after cerebral stroke?” They were then asked to select the 16 most significant parameters from a set of 30 identified by the authors.

The survey was sent by e-mail to 50 physicians and physiotherapists and a total of 25 replies were received.

Next, the 16 parameters necessary for the development of the UBI indicator were selected using the following criteria:

• The percentage distribution of parameters beyond the standard (M1);
• The differences in mean values between the reference group and the patient group (M2);
• The variability of parameters (M3).

2.4.1. Selection of Parameters Taking into Account the Percentage Distribution of Parameters beyond the Standard (M1)

Selection of input parameters was based on the qualification of results obtained for the stroke patients with upper limbs paresis, with up to 4 ranges defined by the mean value and standard deviation obtained from the reference group (

Table 1. Classification ranges of parameter results.

Evaluation of the Results	Colour	Range of Results
Results in the norm	Green	$<\mathrm{mean}\pm \mathrm{std}>$
Results at the limit of the norm	Yellow	$<\mathrm{mean}-2\times \mathrm{std}; \mathrm{mean}- \mathrm{std})\cup (\mathrm{mean}+\mathrm{std}; \mathrm{mean} +2\times \mathrm{std}>$
Results beyond the norm	Orange	$<\mathrm{mean}-3\times \mathrm{std}; \mathrm{mean}-2\times \mathrm{std})\cup (\mathrm{mean}+2\times \mathrm{std}; \mathrm{mean} +3\times \mathrm{std}>$
Results beyond the norm significantly	Red	(−∞; mean−3$\times$std)∪(mean+3$\times$std; +∞)

). The ranges are marked by green, yellow, orange or red, which indicate the difference between the result of a certain parameter obtained for a given patient and the result obtained for the reference group. Boundary values of the ranges were defined using the mean value and standard deviation obtained in the reference group, for both the dominant and non-dominant upper limb, respectively.

Having determined the boundary values of the ranges for each of the 30 parameters, the results obtained for the stroke patients were qualified into individual ranges, separately, for both the dominant and non-dominant upper limb. The subsequent step involved determination of the percentage share of each of the 30 parameters in individual ranges in the stroke patient group. This operation made it possible to show if a given parameter, and to what degree, differentiated from the results obtained for the stroke patients in comparison to the reference group.

All 30 kinematic parameters were sorted in a sequence, from the largest deviation of results from the standard, to the smallest deviation. In other words, a sequence starting from the smallest number of results being within the green range, in compliance with the reference.

Further analysis of the selection parameters for the new indicator considered the 16 most differentiated parameters, for both the dominant and non-dominant upper limb, respectively. From this, two sets of sorted parameters were obtained.

2.4.2. Selection of Parameters Taking into Account the Differences in Mean Values between the Reference Group and the Stroke Patient Group (M2)

This selection method was based on the determination of the difference in the mean values of the analysed parameters between the reference and the stroke patient group. The mean values were determined for all 30 parameters, for both the dominant and non-dominant limb. Following computation of the differences in the mean values, the parameters were sorted from the largest to the smallest difference obtained. Further analysis involved 16 selected parameters which had produced the biggest differences in mean values, for both the dominant and non-dominant upper limb. Accordingly, two sets of sorted parameters were obtained from this method.

2.4.3. Selection of Parameters Taking into Account the Variability of Parameters (M3)

Variability within the 30 parameters in both the reference group and stroke patient group, for both the dominant and non-dominant upper limb, were determined. Variability was defined by means of the variability coefficient expressed in the following way:

$$\mathrm{CV}=\frac{\mathrm{std}}{\mathrm{mean}}$$

(1)

where:

std—standard test deviation,

mean—arithmetic mean obtained in the test.

Next, the ratio of the variability coefficient obtained for each input parameter in the stroke patient group to the variability coefficient obtained in the reference group was calculated:

$$CV\_M{3}_i=\frac{CV\_P{G}_i}{CV\_R{G}_i}$$

(2)

where:

i—subsequent parameters (P1–P30);

CV_PG_i—variability coefficient of given parameter i in patients group PG;

CV_RG_i—variability coefficient of given parameter i in reference group RG.

After computation of CV_M3_i, the parameters were sorted from the highest to the lowest value. Subsequently, the 16 parameters with the highest variability in the stroke patient group in relation to the reference group, for both the dominant and non-dominant upper limb, were selected. From this method, two sets of sorted parameters were obtained.

2.4.4. Final Selection of Parameters

The final step in the selection of parameters for the development of the new indicator was comparison of all 6 sets of parameters, including highlighting the selected 16 parameters. Frequency of appearance of individual parameters was checked in given sets and the parameters that repeatedly appeared in the biggest number of sets were shortlisted. Physiotherapists were consulted with regards these shortlisted parameters, and they were verified according to the results obtained in the survey.

The above-mentioned 16 parameters were then implemented into the mathematical algorithm of the UBI indicator. The values of the new indicator were computed for the reference and stroke patient group, for both the dominant and non-dominant upper limb.

2.4.5. Statistical Analysis

Quantitative variables of the analysed parameters were expressed as mean and standard deviation, as well as minimum and maximum value. Distribution of the analysed variables was assessed for normality using the Shapiro-Wilk test. Analysis of differences in the analysed parameters between groups was performed by Student’s independent-samples t-test, when data was normally distributed or the Mann-Whitney U test for non-parametric data. For within-group analysis, Student’s paired-samples t-test or Wilcoxon signed-rank test was used to check for differences between the dominant and non-dominant upper limb. All statistical analyses adopted significance level p = 0.05. Statistica 13.1 software was used for all statistical analyses.

3. Results

3.1. Selected Input Parameters

Measurement of the kinematics of upper limb movements during the activity of drinking from a mug allowed for the determination of the values of 30 selected temporal and kinematic parameters. Mean values and standard deviations, as well as minimum and maximum values of all parameters in the reference and the stroke patient groups, for both the dominant and non-dominant upper limb, are presented in

Table 2. Results of the 30 selected input parameters for the reference group and the stroke patient group.

Parameter	Reference Group			Stroke Patients Group
	Dominant Limb	Non-Dominant Limb	dl vs. ndl p-Value	Dominant Limb	Non-Dominant Limb
	Mean ± Std (Min–Max)	Mean ± Std (Min–Max)		Mean ± Std (Min–Max)	Mean ± Std (Min–Max)
P1	2.3 ± 0.9 (1.1–5.4)	2.2 ± 0.8 (0.6–4.5)	0.823	1.9 ± 0.8 (0.4–3.9)	2.8 ± 1.7 (0.6–9.1)
P2	2.3 ± 0.6 (1.2–4.1)	2.1 ± 0.7 (1.2–4.6)	0.027 *	1.8 ± 0.6 (1.1–3.4)	2.1 ± 0.6 (1.3–3.9)
P3	46.3 ± 8.2 (26.5–56.3)	43.3 ± 9.7 (18.8–59.6)	0.061	40.79 ± 13.9 (19.2–79.1)	36.2 ± 16.4 (−11–68.1)
P4	80.4 ± 11.5 (58.6–103.6)	75.9 ± 11.4 (51.5–93.2)	0.062	64.4 ± 11.3 (43–84.7)	63.4 ± 15.8 (26–108.4)
P5	24.8 ± 8.8 (7.1–40.9)	29.6 ± 7.7 (16.1–52.1)	0.001 *	18.9 ± 11.7 (−19.8–38.5)	16.6 ± 6.1 (4.1–30.7)
P6	34.9 ± 8.5 (21.4–50.4)	38.7 ± 8.9 (23.5–62.6)	0.002 *	32.3 ± 12.6 (−0.8–54)	29.4 ± 10.9 (11–63.5)
P7	10.6 ± 8.6 (−4.9–30.1)	4.6 ± 9.5 (−15.3–32.2)	0.016 *	20.1 ± 25.1 (−12.9–85.5)	16.3 ± 22.2 (−11.4–75.8)
P8	22.9 ± 10.3 (6.3–41.7)	17.5 ± 9.2 (0.5–41.6)	0.043 *	32.6 ± 24.5 (−0.8–101.4)	30.7 ± 24.8 (6.7–97.8)
P9	77.5 ± 18.6 (42.5–129.2)	81.3 ± 21.3 (41.2–137.8)	0.199	57.4 ± 17 (17.7–100.7)	68 ± 15.6 (43.1–111.4)
P10	128.5 ± 9.9 (102.5–148.1)	134.5 ± 9.5 (115.2–156.2)	0.001 *	108.5 ± 15.2 (76.7–145.1)	131.3 ± 19 (104.2–177.5)
P11	23.2 ± 22.6 (−19.6–58.3)	6.9 ± 24.9 (−36.6–51.7)	0.001 *	61.3 ± 16.7 (29.8–98)	16.9 ± 45.8 (−179.3–113.2)
P12	67.7 ± 24.3 (6.5–119.2)	55.6 ± 22.1 (1.2–83.7)	0.001 *	93.1 ± 17.5 (57.6–133.4)	81.5 ± 32.3 (32.4–179.7)
P13	−23.4 ± 10.4 (−45.1–−4.4)	−21.8 ± 6.8 (−37.6–−7.9)	0.239	−22.5 ± 16.6 (−56.2–20.3)	−19.5 ± 16.4 (−68.8–5.6)
P14	−7 ± 13 (−39.8–19.5)	−2.2 ± 9.3 (−21.8–15.3)	0.012 *	−0.3 ± 17 (−28.5–43.9)	2.2 ± 20.3 (−61–55.9)
P15	−6.6 ± 7.4 (−20.6–11.2)	−11.3 ± 9.5 (−26.9–3.3)	0.004 *	−12.4 ± 12.6 (−51.7–5.1)	−6.6 ± 11.9 (−33.5–23.8)
P16	6.2 ± 7.7 (−6–23.6)	3.3 ± 7.9 (−9.8–17.6)	0.041 *	2.9 ± 14.7 (−33.3–34.4)	11.1 ± 12.5 (−26.4–33.3)
P17	0.1 ± 0.1 (0–0.2)	0.1 ± 0.1 (0–0.3)	0.422	0.2 ± 0.1 (0–0.4)	0.1 ± 0.1 (0–0.5)
P18	0.1 ± 0.1 (0–0.3)	0.1 ± 0.1 (0–0.3)	0.203	0.2 ± 0.1 (0–0.4)	0.2 ± 0.1 (0–0.6)
P19	4 ± 3.3 (0.3–13.8)	3.5 ± 3.3 (0.4–14.1)	0.421	8.4 ± 5.9 (0.3–22.6)	7.9 ± 6.5 (0–30.8)
P20	5.8 ± 3.4 (1.3–16.3)	5.9 ± 3.8 (2.1–18.9)	0.203	11 ± 6.3 (2.7–24.7)	11.5 ± 7.3 (2.5–37.1)
P21	0.1 ± 0.1 (0–0.4)	0.1 ± 0.1 (0–0.4)	0.739	0.2 ± 0.1 (0–0.5)	0.2 ± 0.1 (0–0.6)
P22	0.2 ± 0.1 (0.1–0.5)	0.2 ± 0.1 (0–0.5)	0.043 *	0.3 ± 0.1 (0.1–0.5)	0.3 ± 0.1 (0.1–0.7)
P23	7.6 ± 5.5 (0.8–23.7)	7.4 ± 5.3 (0.7–24)	0.739	12.7 ± 7.1 (1.8–26.5)	11.8 ± 7.2 (1.9–33.7)
P24	9.8 ± 5.4 (3.6–26.4)	10.4 ± 5.9 (2.6–29.6)	0.043	15.8 ± 7.3 (3–28.8)	16.1 ± 8.2 (3.2–40.8)
P25	0.1 ± 0.1 (0–0.3)	0.1 ± 0.1 (0–0.3)	0.267	0.1 ± 0.1 (0–0.3)	0.1 ± 0.1 (0–0.5)
P26	0.1 ± 0.1 (0–0.3)	0.2 ± 0.1 (0–0.4)	0.747	0.1 ± 0.1 (0–0.4)	0.2 ± 0.1 (0.1–0.6)
P27	6.6 ± 4.8 (0.4–17.5)	6.5 ± 4.7 (0.7–19.1)	0.267	5.2 ± 4.8 (0–18.3)	5.6 ± 5.7 (0.2–27.6)
P28	8.1 ± 4.8 (1.6–19.6)	8.3 ± 4.6 (1.9–20.2)	0.043 *	7.4 ± 5.3 (1.2–20.9)	8.5 ± 6.4 (3.2–33.7)
P29	10.1 ± 4.6 (2.5–19)	8.7 ± 4 (3.5–20.4)	0.109	13.3 ± 5.9 (4.6–30.3)	12.8 ± 7.1 (3.9–34.1)
P30	12.3 ± 6.2 (3.8–27.4)	12.2 ± 4.7 (5.7–24.4)	0.848	12.5 ± 5.6 (3.3–29.5)	14.5 ± 6.8 (2.9–41.9)

dl—dominant limb; ndl—non-dominant limb; * p ≤ 0.05; p-value underlined—t-student test for dependent samples, p value not underlined—Wilcoxon test.

. The statistical tests showed differences between movements performed with the dominant and non-dominant limb in the healthy group. Statistically significant differences were noted for 13 of the 30 parameters. No statistically significant differences were noted mostly for the parameters determining spinal movement. This means and confirms the assumption that the movement pattern for the activity of drinking from a cup (performed repeatedly during the day) is different for the dominant and non-dominant limb. This means that that the normative ranges for all parameters analysed should be determined separately for the dominant and non-dominant limb.

Results from the statistical analysis comparing differences between the parameter values obtained for the dominant and non-dominant upper limb are also shown in

Table 3. Differences between the selected input parameters in the reference group and the stroke patient group.

Parameter	Reference Group vs. Stroke Patients Group p-Value Dominant Limb	Reference Group vs. Stroke Patients Group p-Value Non-Dominant Limb
P1	0.011 *	0.098
P2	<0.001 *	0.632
P3	0.010 *	0.005 *
P4	<0.001 *	<0.001 *
P5	0.016 *	<0.001 *
P6	0.714	<0.001 *
P7	0.371	0.006 *
P8	0.164	0.006 *
P9	<0.001 *	0.001 *
P10	<0.001 *	<0.001 *
P11	<0.001 *	0.078
P12	<0.001 *	<0.001 *
P13	0.165	0.765
P14	0.160	0.07
P15	0.052	0.021 *
P16	0.891	<0.001 *
P17	<0.001 *	<0.001 *
P18	<0.001 *	<0.001 *
P19	<0.001 *	<0.001 *
P20	<0.001 *	<0.001 *
P21	<0.001 *	<0.001 *
P22	<0.001 *	<0.001 *
P23	<0.001 *	<0.001 *
P24	<0.001 *	<0.001 *
P25	0.085	0.171
P26	0.291	0.619
P27	0.085	0.171
P28	0.291	0.619
P29	0.008 *	<0.001 *
P30	0.635	0.066

dl—dominant limb; ndl—non-dominant limb; * p ≤ 0.05; p-value underlined—t-student test for independent samples, p-value not underlined—U-Mann Whitney test.

.

Results of the Student’s independent-samples t-tests and Mann-Whitney U-tests, are shown in Table 3. No statistically significant differences were found in the motion of the wrist joint (P13, P14), movements in the lumbar section of the spine (P25–P28) or the motion range in the shoulder joint (P30). However, statistically significant differences between the reference and the stroke patient group were recorded in at least one upper limb.

3.2. Selection of Input Parameters Taking into Account the Percentage Distribution of Parameters beyond the Standard

With reference to the methodology described in Section 2.4.1, input parameter selection was carried out with consideration of the percentage distribution of parameters beyond the standard. Figure 2 and Figure 3 show the percentage distribution of the parameters obtained for the patients in 4 defined ranges (green, yellow, orange and red), for both the dominant and non-dominant upper limbs. On the basis of these results, the 16 parameters with the highest values of deviation from the values obtained in the reference group was applied to both the dominant and non-dominant upper limbs. The selected parameters are collated in

Table 4. Differences between the selected input parameters in the reference group and the stroke patient group.

No.	Dominant Limb		Non-Dominant Limb
	Selected Parameters	Percentage Distribution of Selected Parameters within the Standard (Green Classifier)	Selected Parameters	Percentage Distribution of Selected Parameters within the Standard (Green Classifier)
1	P11	15%	P5	17%
2	P10	17%	P10	25%
3	P4	32%	P4	30%
4	P18	38%	P6	30%
5	P20	38%	P13	35%
6	P2	40%	P16	38%
7	P7	42%	P14	42%
8	P3	47%	P12	42%
9	P17	48%	P17	43%
10	P19	48%	P19	43%
11	P9	50%	P18	48%
12	P6	52%	P20	48%
13	P12	52%	P22	48%
14	P8	54%	P24	48%
15	P22	55%	P3	50%
16	P24	55%	P30	50%

.

Table 4 shows a set of 16 parameters that most differentiated the results obtained for a given patient and the result obtained for the reference group. These are the parameters for which the percentage distribution of selected parameters within the standard (green classifier) was lowest.

3.3. Selection of Input Parameters Taking into Account the Differences in Mean Values between the Reference Group and Stroke Patient Group

This selection method was based on the determination of the difference in the mean values of the analysed parameters between the reference and the stroke patient group (Section 2.4.2). The parameters were sorted from the largest to the smallest difference. Taking into account the differences in mean values between the reference group and the stroke patient group, 16 parameters with the highest values of difference were selected. These parameters were chosen separately for both the dominant and non-dominant upper limb, and are shown in

Table 5. Differences in mean values of parameters selected according to method M2.

No.	Dominant Limb		Non-Dominant Limb
	Selected Parameters	Differences in Mean Values [°]	Selected Parameters	Differences in Mean Values [°]
1	P11	38.18	P12	25.96
2	P12	25.38	P9	13.30
3	P9	20.10	P8	13.24
4	P10	19.93	P5	13.03
5	P4	16.07	P4	12.58
6	P8	9.70	P7	11.67
7	P7	9.51	P11	10.02
8	P14	6.67	P6	9.27
9	P24	5.97	P16	7.82
10	P5	5.85	P3	7.05
11	P15	5.74	P24	5.64
12	P3	5.53	P20	5.57
13	P20	5.19	P15	4.69
14	P23	5.08	P23	4.44
15	P19	4.36	P14	4.44
16	P16	3.30	P19	4.42

.

3.4. Selection of Input Parameters Taking into Account the Variability of Parameters

To account for variability (Section 2.4.3), the 16 parameters with the highest ratio of the variability coefficient obtained for each input parameter in the stroke patient group to the variability coefficient obtained in the reference group ($CV\_M{3}_i$) were selected. The parameters were chosen for both the dominant and non-dominant upper limb (

Table 6. Variability values for the parameters selected according to method M3 for the stroke patient group.

No.	Dominant Limb		Non-Dominant Limb
	Selected Parameters	$\mathit{C}\mathit{V}\_\mathit{M}{3}_{\mathit{i}}$	Selected Parameters	$\mathit{C}\mathit{V}\_\mathit{M}{3}_{\mathit{i}}$
1	P11	3.59	P16	2.12
2	P12	1.92	P7	1.50
3	P21	1.30	P11	1.33
4	P23	1.30	P23	1.18
5	P22	1.19	P21	1.18
6	P24	1.19	P19	1.15
7	P19	1.16	P17	1.15
8	P17	1.16	P9	1.14
9	P30	1.13	P22	1.13
10	P15	1.09	P24	1.13
11	P29	1.03	P2	1.05
12	P18	1.02	P12	1.00
13	P20	1.02	P18	1.00
14	P1	0.88	P20	1.00
15	P28	0.84	P29	0.83
16	P26	0.84	P30	0.82

).

3.5. Final Selection of Input Parameters

Input parameter selection, for the development of the UBI indicator resulted in the creation of six sets for each of the 16 selected parameters. Frequency of appearance of the individual parameters was checked in given sets, and the results are presented in

Table 7. A list of input parameters selected for the development of the new Upper Body Index indicator according to methods M1, M2, M3; frequency of appearance of individual parameter sets and physiotherapists’ guidelines, derived from survey results.

Parameter	M1_R	M1_L	M2_R	M2_L	M3_R	M3_L	NRR	NRR Selected	Survey
P1					✓		1		✓
P2	✓					✓	2		✓
P3	✓	✓	✓	✓			4	✓	✓
P4	✓	✓	✓	✓			4	✓	✓
P5		✓	✓	✓			3	✓
P6	✓	✓		✓			3	✓	✓
P7	✓		✓	✓		✓	4	✓
P8	✓		✓	✓			3	✓	✓
P9	✓		✓	✓		✓	4	✓
P10	✓	✓	✓				3	✓	✓
P11	✓		✓	✓	✓	✓	5	✓
P12	✓	✓	✓	✓	✓	✓	6	✓	✓
P13		✓					1
P14		✓	✓	✓			3	✓	✓
P15			✓	✓	✓		3	✓
P16		✓	✓	✓		✓	4	✓	✓
P17	✓	✓			✓	✓	4	✓
P18	✓	✓			✓	✓	4	✓	✓
P19	✓	✓	✓	✓	✓	✓	6	✓
P20	✓	✓	✓	✓	✓	✓	6	✓	✓
P21					✓	✓	2
P22	✓	✓			✓	✓	4	✓	✓
P23			✓	✓	✓	✓	4	✓
P24	✓	✓	✓	✓	✓	✓	6	✓	✓
P25							0
P26					✓		1
P27							0
P28					✓		1		✓
P29					✓	✓	2		✓
P30		✓			✓	✓	3	✓	✓

NRR—number of repetitive results, M1_R/M1_L—parameter selection due to percentage distribution of parameters out of normal for right (R)/left (L) upper limb; M2_R/M2_L—parameter selection due to differences in mean values between reference and patient groups for right (R)/left (L) upper limb; M3_R_RG/M3_L_RG/M3_R_PG/M3_L_PG—parameter selection due to variation in parameters for the right (R)/left (L) upper limb, in the reference group (RG) and the stroke group (PG).

. From this comparison, twenty-one parameters were identified that were repeated in at least half of the sets (NRR).

Results from the surveys conducted among physicians and physiotherapists identified seventeen parameters that were repeated in at least half of the survey answers (Table 7). The resulting set of 17 parameters selected by physiotherapists and physicians was compared with a set of 21 parameters selected according to the accepted calculation procedures (parameters repeated in at least half of the sets—NRR). This comparison allowed the selection of 13 parameters that appeared in both parameter determination approaches. As it was assumed that the new index would be based on 16 parameters (similar to the GGI index [25]), it was decided that the missing 3 parameters would be indicated by experienced clinicians and physiotherapists. Three additional parameters were then added to the UBI indicator, including temporal parameters P1 and P2 and P29, which represented the scope of abduction/adduction motion of the shoulder joint.

Final selection of the 16 parameters was carried out through consultations with physiotherapists who provide rehabilitation services to stroke patients on a daily basis. The physiotherapists pointed out the following issues:

• For upper limb motion evaluation, it is necessary to select mainly parameters that define maximum joint angles and motion ranges of the joints;
• Kinematic parameters measured for the spine should consider the possibility of detecting compensation movements, which may be a result of limb paresis;
• Appropriate velocity of the performed movement proves physical efficiency and ability of the upper limb.

The set of 16 input parameters selected is presented in

Table 8. Input parameters selected for the development of the Upper Body Index indicator.

No.	Parameter	Name of Parameter
1	P1	Duration of the lifting phase t1 [s]
2	P2	Duration of the lowering phase t2 [s]
3	P3	Minimum flexion/extension angle of the shoulder joint
4	P4	Maximum flexion/extension angle of the shoulder joint
5	P6	Maximum abduction/adduction angle of the shoulder joint
6	P8	Maximum external/internal rotation angle of the shoulder joint
7	P10	Maximum flexion/extension angle of the elbow joint
8	P12	Maximum supination/pronation angle of the elbow joint
9	P14	Maximum palmar flexion/dorsiflexion angle of the wrist joint
10	P16	Maximum elbow/radial abduction angle of the wrist joint
11	P18	Maximum spine anteversion angle
12	P20	Maximum spine rotation angle
13	P22	Maximum spine anteversion angle in section Th1-Th12
14	P24	Maximum spine rotation angle in section Th1-Th12
15	P29	Abduction/adduction motion range of the shoulder joint
16	P30	External/internal rotation motion range of the shoulder joint

.

3.6. UBI Indicator Results

Selected input parameters constituted the input data for the mathematical algorithm of the UBI indicator. The values of the UBI were calculated separately for the reference group and stroke patient group, for both the dominant and non-dominant upper limb. The UBI index value was determined for each of the 3 repetitions performed with the dominant and non-dominant limbs. The evaluated value of the UBI index for the tested person is the average value of these 3 values obtained for subsequent repetitions. These values have been collated in Figure 4 and Figure 5. The error bars indicate the standard deviation of the UBI values obtained for the 3 repetitions performed for each tested person.

The mean UBI values obtained for the reference group did not exceed 21 (Figure 4). However, in the post-stroke group, UBI values are higher than 30 (Figure 5). In 13 patients, the values of the index for at least one upper limb exceeded the value of 100. In four patients, the values are higher than 200 indicating a high deviation of movement from the set norms for the reference group.

The mean value and standard deviation, as well as the minimum and maximum values of the UBI indicator obtained for the reference group have been collated separately in

Table 9. Data obtained for the Upper Body Index indicator in the reference group.

	Dominant Limb	Non-Dominant Limb
mean ± std	13.67 ± 2.40	13.71 ± 3.36
min–max	9.05–18.21	7.18–20.70

, for both the dominant and non-dominant upper limb. The mean values of the UBI index for the reference group were less than 14 for both the dominant and non-dominant hand. The min-max range of the UBI index for the reference group is similar for the dominant and non-dominant limb. The maximum of the UBI index did not exceed a value of 21.

Table 10. Data obtained for the Upper Body Index indicator in the stroke patient group.

	Dominant Limb	Non-Dominant Limb
mean ± std	130.86 ± 75.07	155.58 ± 170.76
min–max	45.85–351.03	30.17–630.59

summarises the results of the UBI index obtained for the group of post-stroke patients (mean value, standard deviation, minimum and maximum value). The mean values of the UBI index for the whole group of patients differed significantly from the results obtained for the reference group, being 130.86 ± 75.07 for the dominant limb and 155.58 ± 170.76 for the non-dominant limb (Table 10). The rather high value of the standard deviation (especially for the non-dominant limb) indicates that the index results in the patient group have a strongly non-Gaussian distribution, i.e., the values for a few patients differ significantly from the other results. The results of the UBI index for the non-dominant limb for four out of 20 patients exceed a value of 300, including two patients exceeding a value of 500. These results indicate a large deviation of the movement pattern from the pattern obtained for the healthy group (Figure 5).

4. Discussion

Despite dynamic development of measurement systems and techniques for the evaluation of the movement of human motor organs, assessment of upper limb motion dysfunctions is still dependent on medical scales and subjective tests. However, the use of indicators as a method of motion assessment has gained much interest in the research community over the last 20 years [14,15,17,18,19,20,21,22,23,24,25,26,27]. Indeed, the development of such indicators has been concurrent with technological advances in the equipment used for capturing kinematics. Ultimately, researchers are aiming to develop a universal indicator that could be used in the assessment of motion pathology for a range of diseases and disorders. Many studies have been conducted into the application of indicators for the evaluation of gait pathology, and some of the most popular indexes, such as GGI, GDI and GPS, have been verified by many research centres [24,25,26,27]. Unfortunately, indicators for upper limb pathology have not gained the same level of attention, however there has been some attention on this issue from the research community. Indeed, the first upper limb indicator, the APS, was developed by Jaspers E. et al. [15] in 2011. Since then, three additional indicators have been defined, namely, PULMI [17,22,23] GULDI and UMDI [18]. All of these upper body indicators were designed based on the same mathematical algorithm used for gait assessment, the GDI [24]. However, it is proposed that the mathematical algorithm of the GGI gait evaluation indicator [25], would be more suitable for development of an indicator for upper limb pathology. Nonetheless, the main challenge of using this algorithm is the appropriate selection of input parameters. With this in mind, this work aimed to develop methodology for optimal parameter selection in order to create a new UBI indicator for evaluation of upper limb motion pathology.

Here, a complex approach to parameter selection was proposed, based on the concept that input parameters should include variables that best differentiate the results obtained in the stroke patient group from those obtained for the reference group. To achieve this, three selection methods were developed that took into account the percentage distribution of parameters beyond the standard (M1), the differences in mean values between the reference group and stroke patient group (M2), and the variability of parameters (M3). This approach revealed the diversity of particular parameters in the reference group and the group of patients with upper limb motor dysfunctions.

In previous studies of indicator development, the methods used for parameter selection were not clearly defined and they were often proposed by the researchers or physicians with reference to a particular group of patients. Indeed, parameter selection for the development of the GGI indicator was tailored to a group of children with cerebral palsy [25,26,27,28]. Though subsequent research has demonstrated that the GGI indicator could be used in the evaluation of gait in other patient groups [29]. Our approach consisted of a complex method of input parameter selection for the purposes of the development of a new indicator, through consultation with physicians and physiotherapists.

Development of the new UBI indicator was achieved through identification of 2 temporal parameters and 14 kinematic parameters, which included minimum and maximum angles of the upper limb joints, motion ranges of the joints and spine movement (Table 9). These parameters assessed motion in the shoulder and elbow joints, in all possible planes, as well as movement of the spine. Furthermore, the selected parameters also encompassed the maximum angle of spine anteversion and rotation of the whole spine and the thoracic region. Inclusion of parameters connected with motion of the spine made it possible to detect movements compensating for limb paresis. Indeed, none of the previously developed indicators of upper limb motion evaluation took spine movement, or movement duration, into consideration when selecting algorithm input parameters [14,15,17,18,22,23].

Development of the APS indicator was achieved solely on the evaluation of upper limbs during gait, whereas the UBI indicator developed made use of 4 parameters describing the movement of flexion-extension and adduction-abduction in the upper limb joints [15]. However, the indicators based on the algorithm of the GDI index, such as PULMI, GULDI, UMDI, did take into consideration alterations in the course of kinematic parameters of motion in the upper limb joints [17,18,22,23,30].

Following selection of input parameters for the new UBI indicator, the values for all participants from the reference and the stroke patient groups were computed. This demonstrated that the UBI indicator was able to detect deviations in the stroke patients, from the reference, in the performed movements. Indeed, UBI values obtained from analysis of the stroke patients were much higher than those obtained from the reference group (Figure 4 and Figure 5).

There were a number of limitations to this work, which had a relatively small sample size and was limited to the inclusion of patients who had suffered an ischaemic stroke. The two groups (reference group and patients) were not age-matched. It is well-known that motor performance decrease with age, so the author cannot exclude that the observed differences in the UBI values between the two groups are consequences of the differences in age instead of stroke. Furthermore, the development of the UBI indicator was conducted under the conditions of a single task, drinking from a mug. Moreover, the results of the UBI index have been presented on the same groups of people used to select the 16 parameters. The 16 parameters were selected with a procedure aimed at fostering the separability between the two groups. So, future research should focus on evaluating UBI on a different and bigger population.

5. Conclusions

This article presented a method for selection of input parameters, which were then used in the development of a new upper limb motion pathology indicator, based on a PCA algorithm. Input data of the UBI indicator included temporal and kinematic parameters, involving minimum and maximum angles of the upper limb joints, motion ranges in the joints and parameters related to the movement of the spine. Furthermore, the new UBI indicator made it possible to detect deviations in movements of the analysed activity from the adopted standard. Therefore, the proposed UBI indicator may find its application in the analysis of any motion sequences performed by the upper limb.

6. Directions for Future Research

Future studies will look to expand the size of the patient cohort and to include participants with motor dysfunction arising from a wider range of disease and injury. The development of the UBI indicator was conducted under the conditions of a single task, drinking from a mug. Undoubtedly, similar investigations should be carried out for other manipulative activities of upper limbs.

Further research should also seek to conduct sensitivity analysis of changes to the proposed indicator values throughout the course of treatment and rehabilitation. Meanwhile, the indicator values should be correlated with other indexes of upper limb motion evaluation or medical scales and tests. Finally, future research should focus on selecting motion sequences that allow for the evaluation of patient’s motor dysfunctions in clinical assessment and the evaluation attempt with the UBI indicator.