Kinematic IMU-Based Assessment of Postural Transitions: A Preliminary Application in Clinical Context

Abstract

This study aims to develop a new methodology for assessing postural transitions, such as sit-to-stand movements, and to preliminarily apply it in a clinical setting. These movements provide valuable information about the state of movement effector system components, whether musculoskeletal, nervous, or cognitive, and their evaluation is a key point in the functional assessment in the clinical setting of patients with complex rehabilitative needs. The objective of this study was developed by pursuing three goals: verifying the ability to discriminate between healthy and pathological subjects, defining a set of parameters for movement assessment, and thus designing a preliminary evaluation paradigm for future clinical applications. We investigated the signals from a single IMU sensor applied to subjects (20 healthy and 13 patients) performing five different postural transitions. A set of six kinematic variables that allowed a quantitative assessment of motion was identified, namely total time, smoothness, fluency, velocity, jerk root mean square, and maximum jerk variation. At the end of the study, the adopted methodology and set of parameters were shown to be able to quantitatively assess postural transitions in a clinical context and to be able to distinguish healthy subjects from pathological subjects. This, together with future studies, will provide researchers and clinicians with a valuable resource for evaluating the results of a rehabilitation program, as well as for keeping track of patients’ functional status in follow-up evaluations.

1. Introduction

Postural transitions (PTs) are the movements that occur during the progression from one posture to another, such as from sitting to standing. Considering a posture as a dynamically stable condition, PTs appear critical since they describe the evolution between two different postures, and therefore involve important kinematic and dynamic transitions [1], unlike postural shifts, which happen as movements or postural adjustments around what could be considered the same stability condition [2]. PTs are one of the essential conditions for performing activities of daily living. Their assessment enables gathering valuable functional information, especially about the state of the movement effector system [3], whether musculoskeletal, nervous, or cognitive. In particular, two aspects are fundamental during the functional assessment of patients with complex rehabilitative needs in a clinical setting: the ability of the subject to perform these movements safely without supervision or with help, and in a time valuable for the performance of the task.

Many clinical outcome scales and questionnaires contain the assessment of a single or, at most, a couple of PTs among their items [4,5,6]. Among these, those of main rehabilitation interest, according to our clinical expertise and preliminary data, and also the most widely used for the functional assessment of patients in clinical practice, are sit to stand (SiSt), stand to sit (StSi), sit to supine (SiSu), supine to sit (SuSi), and roll (Roll). These five PTs represent excellent simulation of challenging activities for static and dynamic balance, as well as the possible postural variations required during the performance of activities of daily living (ADLs). These five PTs can be considered fundamental transitions that often occur, including in combination, in more complex tasks. Therefore, the main advantage is that with these five PTs, we can assess a patient’s ability to perform complex movements in their environment. Limitations in accomplishing or the inability to accomplish one or more of these PTs could severely affect the lives of patients in all ICF (International Classification of Functioning, Disability and Health) care settings [7].

Different technologies have been developed and applied to the assessment of movement [8,9,10,11,12] and thus also to postural transitions [13,14]. These include the use of accelerometry, particularly that implemented in IMUs (Inertial Measurement Units), which enables reliable analysis and simple, non-intrusive, on-subject application with a relatively low cost of production and use. These types of sensors are widely found in the literature, with the set-ups differing by the number of devices used, with single [15] or multiple sensor applications [16], and the different positioning strategies and locations on the body of the analyzed subjects (e.g., head, sternum, spine, or lower limbs) depending on the aim of the analysis and in general on the assessment conditions [17,18,19].

Due to its ease of use and immediacy in providing result data, IMU-based technology lends itself to motion analysis for multiple purposes, such as gait analysis [20], the instrumentation of field tests [21,22], and monitoring ADLs or subject performance [23].

However, the sensor location strongly affects the quality of the raw signal and may alter the natural movement performed by the subject. Therefore, different acquisition protocols are typically designed to evaluate different tasks, optimizing the sensor location to minimize its possible drawbacks [24].

While this approach surely improves the quality of the signals, it is also poorly suitable for those applications oriented toward continuous monitoring or multi-task assessment. In these cases, the protocol should foresee a fixed positioning of the sensor, which favors the possibility of the subject performing all the required movements over the data quality. Important interventions may be required in the data post-processing to overcome the consequently introduced technical limitations. In other words, the complexity of the procedure is shifted from the acquisition phase to the data elaboration. This complexity increases when the target tasks are particularly dissimilar, like SiSt, SuSi, and Roll.

Moreover, to the best of our knowledge, no IMU-based evaluation method has ever been proposed to analyze all five PTs mentioned above without modifications to the sensor location or adjustments in the data processing among the PTs.

In our study, we chose a single body-attached IMU set-up applied to the trunk during the execution of PTs by a population of healthy subjects and a mixed sample of patients with rehabilitative needs. For the signal processing and data analysis, we modified and adapted the methodology used by Bagalà et al. [25]. In their work, the authors presented a set of functional parameters for the assessment of a postural transition. However, the task considered was a complex transition, i.e., lie to sit to stand to walk. For this reason, only some of those parameters may be reasonably applied to the assessment of other PTs, and adaptations to their definition may be expected. A set of modified parameters, less prone to time dependency, was proposed in a previous work by Amici et al. [26] that only focused on the analysis of sit to stand: the current work inherits that knowledge, improving the study and extending it to the different PTs.

This study, therefore, has multiple aims: (i) to preliminarily verify the ability of our single-IMU set-up to differentiate a population of healthy subjects from one of pathological subjects, (ii) to define meaningful, rigorous, and task-independent parameters for movement assessment in a clinical context during PT execution, and thus (iii) to design and propose an exploratory evaluation paradigm that lays the foundation for future clinical applications.

2. Materials and Methods

Data were collected from May to July 2019 through a custom designed-acquisition campaign. The ethical committee of IRCCS Fondazione Don Carlo Gnocchi approved the study (n.FDG_21.6.18), which was conducted according to the Declaration of Helsinki.

2.1. Population

A population consisting of healthy and pathological volunteers was considered for enrollment. All the recruited subjects provided written informed consent.

Different inclusion criteria were adopted for the two subsets of healthy and pathological subjects. The inclusion criteria for the healthy subjects were (i) adults, (ii) both sexes, and (iii) the absence of past or present pathologies that could affect their movement presently. The inclusion criteria for the pathological sample were instead (i) adults, (ii) both sexes, (iii) recruitment within the first week of rehabilitation, and (iv) prescription for the rehabilitation of postural transitions.

The subjects included in the pathological subset may therefore have been affected by different pathologies. Given the observational and preliminary nature of the study, no a priori sample size was calculated, but nonetheless, the enrolled sample size was chosen according to previous studies in the field [27], predicting at least 10 subjects for each group (i.e., healthy and pathological).

2.2. Acquisition Protocol

The five PTs (tasks) schematized in Figure 1 were evaluated for each subject:

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Sit to supine (SiSu). From a sitting position at the bed border, with their hands on their thighs, the subject is required to lay supine.

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Supine to sit (SuSi). The subject is required to perform a transition from lying supine, with their hands by their sides, to a sitting position at the bed border. The subject is free to move their arms to perform a natural transition.

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Sit to stand (SiSt). Starting from a sitting position at rest, with their hands on their thighs, the subject is required to perform a transition to a standing position.

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Stand to sit (StSi). From a standing position, the subject is required to perform a transition to a sitting position.

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Roll (Roll). From a supine position, the subject is required to roll onto their left side until resting on their left shoulder, return to the supine position, repeat the rotation in the opposite direction until resting on their right shoulder, and return to the supine position.

For all the tasks, the movement is performed at a self-imposed velocity, and the subject is required to stay still in the initial and final poses for at least a couple of seconds. The operator provides a “go” signal to indicate that acquisition has begun, but the subject freely decides when to actively begin the transition. No additional indications or constraints to the motion performance were provided to the subjects (e.g., the subjects could use their arms or hands to help with PT execution).

Each task was repeated at least three times by each subject, and the time elapsing among the acquisitions was used by the assessors to save the data: the final dataset is therefore composed of 495 acquisitions.

2.3. Experimental Setup

The experimental setup used for the acquisition campaign consisted of a standard physiotherapy bed, 46 cm off the ground, and the Inertial Measurement Unit (IMU) G-sensor 2 (BTS Bioengineering S.p.A., Garbagnate Milanese, Milan, Italy). The IMU was placed on the subject’s trunk by a trained operator, aligning the superior edge of the sensor box with the proximal edge of the manubrium sterni and fixing it to the body with biocompatible tape. Figure 2 depicts the location of the sensor and the convention adopted for the reference frame.

This IMU is wireless and includes both a triaxial accelerometer and a triaxial gyroscope, with tunable sensibility. For the current purposes, sensibility was set to ±2 for the accelerometer and ±2000°/s for the gyroscope. To enable data fusion, according to the sensor datasheet, an acquisition frequency of 200 Hz was set. The IMU sensor must be calibrated before each new acquisition to perform the correct measurement. The calibration procedure requires that the sensor be held on a stable surface for a few moments until the sensor itself provides a feedback signal indicating that the calibration was successfully completed. However, this procedure was poorly consistent with the needs of the applied acquisition protocol. The required calibration procedure was therefore performed with the sensor already in place, with the subject remaining still at the beginning of the acquisition for the necessary amount of time.

2.4. Data Analysis

Data collected by the gyroscope and the accelerometer of the IMU sensor were extracted and imported into MATLAB^® (MATLAB R2023b, The MathWorks, Inc., Natick, MA, USA) environment for custom data processing.

For each repetition of each task, the total angular velocity ω was computed as the vector sum of the triaxial components of angular velocity ω_i (i = 1, 2, 3) detected by the gyroscope. Likewise, the triaxial acceleration signals were combined (vector sum) into the total acceleration a. The jerk signal j was computed from a, applying a custom two-point derivative approximation.

According to the literature, in the acceleration signal of a body in motion, two components can be identified: a first component due to the presence of gravity, which Bagalà et al. [25] define as a_g, and an additional component due to bodily motion, namely a_b in the same paper [25]. In their work from 2006 [28], Karantonis et al. state that only the gravitational component of the acceleration signal of a body moving in space should be evaluated when aiming at measuring its postural orientation. This contribution is described by Bagalà et al. as a trend line. The literature depicts that movements typical of the activities of daily living like gait present a frequency between 0.8 Hz (or even 0.6 Hz in some sources) and 5 Hz [13,25,28]. The signals were therefore low-pass-filtered with a cut-off frequency set at 5 Hz, applying a fourth-order zero-phase low-pass Butterworth filter, and then detrended. This detrended filter acceleration signal was then filtered by applying an additional fourth-order zero-phase low-pass Butterworth filter, with the cut-off frequency set at 0.6 Hz, to isolate a_g, the gravitational contribution to the signal. The acceleration due to bodily movement, a_b, was identified by the difference as the remaining part of the detrended filter acceleration signal not included in a_g.

Subsequently, the portion of the signal corresponding to the actual movement was identified for each acquisition. The instants identifying the events of the start and end of the movement were detected in the a_g signal, applying an improved version of the method described in Amici et al. [26]. The procedure involves the implementation of a simplified version of the double window approach for the detection of the transient values in EMG signals presented in Amici et al. [29]. According to this method, the signal is swept with a moving observation window (OW) of 0.2 s, which moves by 1 index step, to identify the interval presenting the minimum standard deviation. This OW corresponds to the rest condition of the subject, and the mean value OW_mean of this interval is computed. The start and end of the movement are then defined as a detectable variation in the acceleration value with respect to the OW_mean value. The start and stop events are in fact identified, respectively, as the first and last instants of the signal presenting a variation in the acceleration value beyond the threshold 0.003·OW_mean. This threshold value was the result of a fine-tuning process of the identification algorithm and proved the most stable results in all the testing conditions.

2.5. Functional Parameters

For the performance analysis of the PTs, the set of parameters presented by Amici et al. [26] was applied.

Table 1. Definition of the adopted functional parameters (Adopted Definition) and of the reference parameters described in the literature (Traditional Definition, by Bagalà et al. [25]), according to the current notation. For the additional parameters RMS_j and Δj, j is evaluated within the time interval [start; stop].

Parameter	Adopted Definition	Traditional Definition (_B)	Measurement Unit
			Adopted Definition	Traditional Definition
Total Time (TT)	TT = Stop − Start		[s]
Smoothness (J)	$J={\displaystyle \frac{1}{TT}}·{\displaystyle \sum _{t=Start}^{Stop}}\left|j_t\right|$	$J_B=ln\left({TT}^3·{\displaystyle \sum _{t=Start}^{Stop}}\left|j_t\right|\right)$	[m/s4]	[m]
Fluency (Fl)	$Fl={\displaystyle \frac{1}{TT}}·{\displaystyle \sum _{t=Start}^{Stop}}\left|{a_b}_t\right|$	${Fl}_B=ln\left({TT}^2·{\displaystyle \sum _{t=Start}^{Stop}}\left|{a_b}_t\right|\right)$	[m/s3]	[m]
RMSG	${RMS}_G={\displaystyle \frac{1}{3}}·{\displaystyle \sum _{i=1}^3}rms\left({\omega }_i\right)$	${RMS}_{G\_B}=\sqrt{{\displaystyle \frac{{\sum }_{t=start}^{stop}{{\omega }_t}^2}{f_s·TT}}}$	[°/s]
RMSj	${RMS}_j=rms\left(j\right)$	-	[m/s4]	-
Max. Jerk Variation (Δj)	$\Delta j=j_{max}-j_{min}$	-	[m/s4]	-

shows the adopted parameters and their definitions: total time TT, smoothness J, fluency Fl, movement velocity RMS_G, jerk root mean square RMSj, and maximum jerk variation Δj. In particular, the parameters smoothness J, fluency Fl, and movement velocity RMS_G were designed according to a modified version of the formulas proposed by Bagalà et al. [25] in terms of their set of indicators, time TT maintained its traditional definition, whereas the last two parameters were additionally evaluated. In the method proposed by Bagalà et al. [25], an additional parameter was also presented, defined as rotational speed and evaluated based on the jerk signal. Since the definition of this parameter depends on a condition of trunk tilt, which could not occur in some of the PTs under investigation, this parameter was excluded from the current set of parameters.

In more detail, the considered set of parameters is composed of the following:

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Total time TT: this parameter quantifies the time actually elapsed from the beginning to the end of the movement, detected according to a repeatable strategy. TT also represents the normalizing factor for all the other parameters.

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Smoothness J: This parameter investigates how much the movement is disrupted, assessing the evolution of the acceleration in time in terms of jerk.

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Fluency Fl: This parameter quantifies the acceleration due to the bodily motion during the movement without considering the acceleration contributions generated by the actual focal movement, described by a_g.

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Movement velocity RMS_G: This parameter combines the RMS values of the three components of the angular velocity measured during the movement.

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Jerk root mean square RMSj: This parameter computes the RMS value of the jerk signal between the start and stop instants of the movement.

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Maximum jerk variation Δj: This parameter measures the difference between the maximum and minimum values assumed by the jerk signal during the movement.

2.6. Statistical Analysis

The values of the six adopted parameters and of the three reference parameters from the literature, J_B, Fl_B, and RMS_{G_B}, were computed for all acquisitions. The mean value for each of the parameters was calculated for each task (three repetitions of each PT for all subjects). Descriptive statistical analysis was then performed on the obtained data (mean ± standard deviation). Non-parametrical analysis was performed on the data, as the number of subjects in the included population was too low. Mann–Whitney test was performed on the parameters to test the presence of statistically significant differences between the healthy and pathological samples for each approach. No comparisons between the two approaches were performed. The computation was performed with the values obtained applying the parameter definitions adopted in this study and with the values of J_B, Fl_B, and RMS_{G_B} calculated according to their literature definitions [25] for comparison. For the interpretation of the results, a significance level of 5% was considered. Finally, the presence of correlation among the adopted parameters in the two populations of healthy and pathological subjects was investigated through a correlation matrix (Spearman’s Rho) and evaluated according to the conventions presented in

Table 2. Conventions used to define the correlation strength between parameters.

	Very Weak	Weak	Moderate	Strong	Very Strong
Correlation	0.000–0.199	0.200–0.399	0.400–0.599	0.600–0.799	0.800–1.000
Color Convention

The color of each cell in line 2 refer to the correlation values within the range in line 1. This color convention is also applied for values in Table A1, Table A2, Table A3, Table A4, Table A5, Table A6, Table A7, Table A8, Table A9 and Table A10.

.

3. Results

A total sample of 33 subjects were enrolled, consisting of 20 healthy and 13 pathological subjects. The pathological population was composed of heterogeneous pathologies: eight post-stroke survivors, two subjects affected by Guillan–Barrè–Strohl syndrome, one person with multiple sclerosis, one subject with paraparesis, and one outcome of laminectomy. Descriptive data for each population are provided in

Table 3. Description of the distribution of the analyzed samples by gender, age, height, and weight for the subsets of healthy and pathological subjects and for the overall population. Data are presented as mean value ± standard deviation except for in the gender column.

Sample	Gender (Males, Females)	Age [Years]	Height [m]	Weight [kg]
Healthy	15, 5	23.3 ± 2.2	1.77 ± 0.08	73.0 ± 12.4
Pathological	10, 3	65.8 ± 16.6	1.70 ± 0.06	71.4 ± 8.5

.

Figure 3 and Figure 4 present an example of the detrended filtered acceleration signal for the healthy and the pathological subject, respectively. The gravitational component a_g and the bodily motion component a_b of the acceleration are also depicted, as well as the detected start and stop events. Appendix A.1 of Appendix A contains examples of these signals for all the investigated PTs.

The obtained values of the functional parameters for all the analyzed PTs are shown in

Table 4. Values (mean ± standard deviation) of functional parameters in the healthy and pathological populations of all considered PTs.

			Traditional Definition (_B)			Adopted Definition
PT	Condition	Total Time TT [s]	Smoothness JB [m]	Fluency FlB [m]	Velocity RMS RMSG_B [deg/s]	Smoothness J [m/s4]	Fluency Fl [m/s3]	Velocity RMS RMSG [deg/s]	Jerk RMS RMSj [m/s4]	Max Jerk Variation Δj [m/s4]
Roll	Healthy	6.69 ± 0.83	14.41 ± 0.42	9.53 ± 0.32	52.14 ± 14.04	987.90 ± 298.64	49.60 ± 14.25	52.12 ± 15.03	7.13 ± 2.37	59.02 ± 28.55
	Pathological	11.38 ± 3.74	15.89 ± 1.11	10.49 ± 0.80	63.72 ± 12.84	634.17 ± 276.08	31.37 ± 14.44	63.70 ± 12.84	4.60 ± 2.04	41.22 ± 16.65
SuSi	Healthy	3.44 ± 0.42	11.80 ± 0.48	7.79 ± 0.36	60.71 ± 20.16	1052.85 ± 288.64	65.28 ± 18.29	60.67 ± 20.15	7.40 ± 2.31	46.31 ± 16.41
	Pathological	5.26 ± 1.39	13.05 ± 1.03	8.58 ± 0.79	75.67 ± 23.08	779.13 ± 312.50	45.48 ± 19.46	75.63 ± 23.07	5.48 ± 2.47	38.75 ± 20.93
SiSu	Healthy	3.14 ± 0.42	11.80 ± 0.60	7.73 ± 0.46	60.46 ± 35.79	1546.46 ± 384.68	81.06 ± 20.65	60.41 ± 35.77	12.40 ± 3.96	92.55 ± 39.77
	Pathological	4.58 ± 1.57	12.68 ± 1.01	8.32 ± 0.72	60.04 ± 14.42	990.67 ± 461.50	55.19 ± 24.62	60.00 ± 14.41	7.63 ± 3.98	60.06 ± 36.40
SiSt	Healthy	3.16 ± 0.18	11.51 ± 0.33	8.02 ± 0.32	87.40 ± 34.41	1054.39 ± 263.78	101.59 ± 29.36	87.33 ± 34.38	8.75 ± 2.59	54.17 ± 17.77
	Pathological	3.44 ± 0.69	11.55 ± 0.63	7.73 ± 0.50	103.10 ± 31.98	855.32 ± 233.88	64.74 ± 23.40	103.03 ± 31.96	6.66 ± 2.37	42.69 ± 17.85
StSi	Healthy	3.01 ± 2.29	11.26 ± 0.43	7.67 ± 0.33	86.30 ± 30.38	1018.24 ± 276.98	82.19 ± 18.95	86.03 ± 30.38	8.28 ± 2.96	53.87 ± 26.69
	Pathological	3.62 ± 0.89	11.62 ± 0.85	7.62 ± 0.60	104.80 ± 48.24	797.66 ± 244.94	51.42 ± 16.34	105.12 ± 48.74	6.71 ± 2.33	51.19 ± 22.45

, and their distribution is presented in boxplots in Figure 5. The values were computed according to both methods in the healthy and pathological populations and are presented as mean ± standard deviation values.

The correlation matrix between the parameters in the two populations showed differences between the two methods considered. In particular, the method proposed by Bagalà et al. [25] showed a higher dependency of smoothness J_B and fluency Fl_B with respect to the task total time TT for both healthy and pathological conditions; this behavior was maintained for all PTs (minimum value of correlation for healthy subjects ρ = 0.520, minimum for pathological subjects ρ = 0.505). The relation between the other parameters showed a very strong correlation between the smoothness and fluency parameters for both methods. Moreover, RMS_j and Δj showed very strong correlations in all PTs. Appendix A.2 of Appendix A shows all the correlation values between the parameters and scatter plots for smoothness and total time correlation.

4. Discussion

This preliminary study presents a postural transition (PT) evaluation process that has clear strengths: the first of them is its simple set-up. The choice of an IMU sensor for motion analysis offers, in fact, several advantages: this technology is easy to use, even by clinicians who work with patients on a daily basis; cost-effective; non-invasive for patients; and applicable directly to the patient without the need for a lengthy preparation time for the subject or the environment (e.g., undressing and placing markers on the subject or a lengthy time for instrument calibration). Moreover, the use of a single IMU sensor with a properly selected location further reduces the impact of the set-up on the subjects’ freedom of movement, allowing natural performance of different tasks and therefore enabling the outline of a framework compatible with the needs of continuous monitoring of a subject’s movement condition. The chosen position for the placement of the sensor represents, in this sense, a good compromise between the capacity of the sensor to properly read the desired signal on the one side and the invasiveness of the IMU sensor for the user on the other across all the performed PTs. Other positioning strategies could provide better results if considering a specific PT only.

Focusing on the analysis of the collected signals, a second relevant key point is in the proposed data processing, which implements an automatic detection strategy for the identification of the start and stop events for the movement that could be applied to all the PTs evaluated. The method is based on the analysis of a_g, i.e., the gravitational contribution to the acceleration signal, which provides information about the focal movement performed by the subject, meant as the main movement, i.e., the specific PT, that the subject is realizing. This strategy proved to be a reasonably robust procedure for the analyzed PTs: in fact, the a_g signal also revealed good results in start and stop detection for acquisitions affected by non-ideal effects, like in the presence of noise or thorax movements due to heartbeats or breathing cycles (see Figure 6).

Nevertheless, Figure 3 and Figure 4 depict that the subject may still make movements, likely representing postural adjustments, also beyond the end of the focal movement, i.e., beyond the end limit for the estimation of the total task time TT. These additional movements, visible in the a_b components, are therefore currently neglected in the computation of the Fl parameters given our purpose of normalizing all the parameters for TT to make them comparable among subjects and repetitions. Alternative methods for estimating the movement time could be adopted in an attempt to overcome this limitation, but our preliminary studies on the current dataset were not particularly promising: involving evaluations of the a_b component to identify stop events made the detection procedure less effective and reliable, significantly affecting the comparability of all of the parameter values, also among repetitions. Investigations to improve the quality of the start–stop detection for all the PTs are currently underway. However, the adoption of a wider dataset of signals could represent, in this sense, a fundamental step. A possible alternative approach could, on the contrary, focus on the definition of an additional parameter that quantifies the assessment time from a_b, as the time elapsed to reach the stability condition from the end of the focal movement as detected from a_g.

The close attention to the optimal identification of the start and stop events is therefore justified for two main reasons: on the one side, this step fosters the repeatability of the overall process, and on the other, it enables improving the accuracy of the assessment procedure, as the position of the start and stop events affects the definitions of all of the parameters, both those currently adopted and from the literature.

Furthermore, distinguishing between gravitational and bodily components a_g and a_b allows two different kinds of evaluations: the analysis of a_g provides information about the kind of focal movement performed by the subject, capturing the pattern associated with the specific PT, and so could be used as a valuable reference for feature extraction, for classification strategies that can distinguish which PT has been performed. On the other side, the a_b component enriches the description of the movement by adding detailed information content that provides insights into how the PT is performed in terms of fine motion control capabilities and the subjects’ coordination. In fact, this analysis allows investigating additional movement, seen as additional acceleration activity, that the subject is performing besides the movement required for the execution of the specific PT (described by a_g instead). Accordingly, the a_b component is evaluated when assessing the fluency of motion within the Fl parameter.

Fl can therefore be meant as an indicator describing a subject’s difficulty in maintaining functional movement while carrying out a PT; in comparison, the smoothness parameter J also informs us about the qualitative aspects of movement but gives a more comprehensive indication of a subject’s difficulty in performing the PT.

The smoothness parameter J can be meant as a synthetic, indirect indicator of the overall amount of movement performed by a subject since it quantifies the variations in the jerk signal during a PT.

The assessment of the velocity is performed through the parameter RMS_G, which represents a well-established summary performance indicator in clinical practice and is typically evaluated together with time-related parameters to infer considerations about the quality of a subject’s functional movement.

Apart from TT, the parameters mentioned above were computed according to traditional definitions [25] and the new adopted definitions. While formal and insubstantial diversities can be identified between RMS_{G_B} and RMS_G, relevant differences emerge for the smoothness and fluency parameters J and Fl between the two methods. The main dissimilarity lies in the way the total time TT is managed.

Both methods aim to make the parameters time-independent. The traditional approach favors the ease of use of the parameters, multiplying the core element of each formula, a summation on the time of jerk or the a_b components, for the third and second power of the TT interval, respectively, and then applying the operator of a natural logarithm; in this way, the final parameter is simplified into a (typically fairly manageable) value in meters. Such a quantity is quite straightforward to interpret: we expect that the lower the value, the better the performance since fewer nonessential movements will have been performed during the execution of the task. In this sense, Table 4 presents data that are actually in line with this expectation for longer and most complex PTs, i.e., Roll, SiSu, and SuSi. The remaining SiSt and StSi PTs reveal comparable results in terms of the mean values for healthy and pathological populations. Although it is very easy to use, this kind of approach could present a weakness in the use of TT as a simplification factor, especially if involved with multiple powers, since the elapsed time may itself be a relevant indicator of the quality of a PT.

The adopted new definition therefore tries to overcome this possible limitation by applying an opposite strategy, i.e., by normalizing the same core elements of the J and Fl formulas with respect to the total time TT. This alternative definition introduces some non-negligible effects: the measurement units of the two parameters are less user-friendly, and similarly, their final values may be more difficult to handle, as the sensitivity of the clinician to these quantities could be less immediate. On the other side, though, these definitions allow obtaining parameters independent of time, which are therefore comparable across subjects, repetitions, and tasks and rigorously describe the kinematic characteristics of the performed laws of motion (variation in jerk and bodily motion component of the acceleration).

Quite unexpectedly, the values obtained with the analyzed dataset reveal that the normalized smoothness and fluency J and Fl are higher for healthy subjects for all the PTs. This result could simply be due to the limitations of the analyzed populations or, on the contrary, could be a hint at further functional considerations. For instance, it could be suggested that the enrolled healthy subjects are able to perform more compensatory adjustments during a PT than the patients in the pathological population. Equally, this consideration also seems to be supported by the results for the final two parameters, i.e., the jerk root mean square RMS_j and its maximum variation Δj; in fact, for the current dataset, both indicators present higher values for the healthy subjects for all the PTs, and this should imply a higher activity in the variation of the jerk, both in terms of frequency and amplitude of the signal.

However, the current population subsets present limitations in their composition: as Table 3 describes, the healthy sample is composed of young adults, whereas the pathological sample is more inclusive but presents a remarkably higher mean age. Kinematic differences in movement execution are described in the literature for sit to stand due to both age [30] and gender [31]. Nevertheless, to the best of our knowledge, no studies have addressed these differences for the other PTs investigated in this study. We are aware that differences due to age may be even more pronounced if we add the presence of disease in either group. At this exploratory stage, the aim of this study was to propose parameters that were not very time-dependent and to test their ability to distinguish between two populations. Undoubtedly, future work will need to address these limitations with populations better matched for age and pathology or functional limitation.

Physical fitness level was not recorded and considered in this study, even if it could play a role in the performance of healthy subjects. In particular, PTs would be performed at the maximum speed and not at a self-selected speed, as in this study. However, our aim was to assess differences within a pathological group and not the intra-differences in the healthy group, which should be analyzed in further studies. Similarly, the composition of the pathological population is heterogeneous by pathology, and the comparison between the two groups could be affected by these aspects. However, the pathological group represents a sample of patients included in a rehabilitation program with difficulties in executing postural transitions. Future studies could investigate the normality values of the parameters and whether the acceleration metrics in pathological conditions deviate from normal parameters or not. Their generalizability in a clinical context is quite good, even if future developments in the field could widen the results and expand them to specific populations (e.g., stroke survivors or Parkinson’s patients).

The limited number of subjects in the two samples of healthy and pathological populations also required us to perform a non-parametrical statistical analysis. The p-values from the Mann–Whitney test reported in

Table 5. p-values of functional parameter differences between healthy and pathological populations; significant results are reported with (*).

Method	Functional Parameter		Roll	SiSt	StSi	SiSu	SuSi
	Total Time	TT	<0.001 *	0.376	0.019 *	<0.001 *	<0.001 *
Traditional Definition (_B)	Smoothness	JB	<0.001 *	0.754	0.167	0.009 *	<0.001 *
	Fluency	FlB	<0.001 *	0.053	0.985	0.009 *	<0.001 *
	Velocity RMS	RMSG_B	0.034 *	0.094	0.311	0.217	0.034 *
Adopted Definition	Smoothness	J	0.005 *	0.053	0.010 *	0.001 *	0.005 *
	Fluency	Fl	0.003 *	0.001 *	<0.001 *	0.004 *	0.003 *
	Velocity RMS	RMSG	0.034 *	0.094	0.277	0.217	0.034 *
	Jerk RMS	RMSj	0.008 *	0.021 *	0.053	0.002 *	0.008 *
	Max Jerk Variation	Δj	0.049 *	0.068	0.985	0.019 *	0.049 *

reveal the presence of statistically significant differences between the healthy and pathological samples for all parameters only in the Roll and SuSi PTs. Velocity was not able to discriminate between the two populations for the other PTs with both definitions, nor the total TT in the case of the SiSt PT. Comparing the performance of the parameters defined according to the two methods, smoothness J and fluency Fl as calculated with the new definition performed better than the corresponding J_B and Fl_B from the literature in detecting statistically significant differences between the healthy and pathological samples for the StSi PT, as well as for the SiSt PT in the case of fluency Fl.

The correlation results of the Spearman’s Rho test reveal lower values of correlation with the total time TT for the parameters J and Fl (adopted definition) than for J_B and Fl_B (traditional definition); this occurs for all the PTs and in both populations of healthy and pathological subjects.

Finally, the possibility of describing a PT with six parameters itself represents a further strength point. In fact, the set of identified parameters is limited in number, but the selected indicators are clinically meaningful and rigorous from a technical–mathematical point of view (i.e., non-dependent parameters), so they could be used to describe the movement in all the investigated PTs. Further study should analyze the possible collinearity among the parameters to allow for a consequent reduction in the number of parameters involved. Besides pure numeric considerations, we expect that this analysis would also consider additional elements, like the functional meaning of a parameter and its readiness for use by clinicians. In fact, the use of redundant parameters might be acceptable if a full set provided information more readily usable by clinicians. However, the quality of PTs is typically assessed in clinical practice with direct observation by trained operators, with functional assessments, and with subjective rating [32,33,34]. The adopted set of parameters helps clinicians to quantitatively assess the qualitative evaluations that they typically infer from the evaluation of a PT; however, further study should also verify possible existing correlations between the presented parameters and clinical outcome scales. This kind of approach can offer higher objectivity than conventional methods [25] and provides the possibility of assessing fine aspects of performance, such as discriminating between fluency, focusing on the control of the body motion by the subject, and smoothness, evaluating the overall movement, as a law of motion.

5. Conclusions

Referring to the three main aims of the work, the results of the analyzed data suggest the following:

  i.

The proposed experimental set-up, with a single IMU, allows investigating all of the proposed PTs and enables us to distinguish a population of healthy subjects from a population of subjects with pathological or abnormal changes in movement.

 ii.

The set of the six evaluated parameters proposes rigorous indicators of the movement kinematics and allows task-independent descriptions of movement. The three parameters smoothness J, fluency Fl, and velocity RMS_G revealed lower values of correlation with the other parameters, especially total time TT.

iii.

The combination of the experimental setup, data processing, and adopted functional parameters may represent a promising framework toward the implementation of strategies for the continuous monitoring of subjects. This evaluation paradigm could, for instance, allow understanding, through machine learning processes, which postural transitions were performed by a subject and in what manner, thus premising, for example, domiciliary monitoring of subjects at risk of falls.

Nonetheless, some limitations still need to be overcome, and further analyses and perspectives are currently ongoing in this direction, in particular investigating aged-matched populations, exploring intra-group differences within healthy populations (e.g., differences related to subjects’ sex), and focusing the research on subjects affected by Parkinson disease within a rehabilitation program. By addressing these areas, future research can refine and expand upon our conclusions, investigating possible optimization of the overall procedure and potentially leading to more precise and tailored assessments of postural transitions, with the final aim of validating and increasing the degree of the generalizability of these first findings.