**1. Introduction**

Modern lifestyle is more and more characterized by the fact that people are moving less and are spending an increasing amount of time sitting [1–4]. This takes into account the time spent working in front of a PC or using means of transportation to move from one place to another. Many leisure activities are also performed while seated (e.g., reading a book, watching television).

A sedentary lifestyle is dangerous for many reasons. It may lead to the development of chronic diseases (e.g., cardiovascular) [5,6] and may also affect psychological health [7]. Another problem related to the increase of time spent sitting is that the position adopted on the chair is often incorrect, thus creating health problems such as back pain [6] and headaches [7].

In recent years, people have become more aware of these problems. This is witnessed by the commercialization of height-adjustable sit–stand desks, but also by the spread of many low-cost devices such as smart watches (e.g., Fitbit trackers, Apple watches) and applications (e.g., Stand Up! The Work Break Timer, Time Out) that push the users to perform micro-breaks every 20–30 min of continuous sitting. In this regard, Sitting Posture Monitoring Systems (SPMS) have been introduced in the community, with the objective of detecting and understanding the position of a person in the seated position.

SPMS can rely on different technologies, which span from the use of wearable sensors [8–13], to the use of cameras [14–16], and also to the use of optoelectronic systems [17]. In all the considered cases, the aim is to provide the user with a minimally intrusive experience, so that the SPMS does not interfere with the normal behavior.

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Among the available solutions, a state-of-the-art solution is that of equipping chairs with sensors able to collect data on the posture of the user [18–21]: Ishac et al. in [18] presented a cushion to be used in the backrest of the chair. The cushion is equipped with a pressure sensing array that allows the measurement of the pressure at 9 different points. The lack of information about the pressure on the seat reduces the amount of information that can be extracted.

Zemp et al. in [19] used an innovative approach based on machine learning to classify the data collected by 16 pressure sensors located on different parts of a chair (armrest, seat and backrest). While allowing an improved posture classification, the computational complexity of this algorithm is quite high.

Similarly, Roh et al. in [20] inserted load cells in the frame of the chair to record data that are processed through a machine learning approach. In this work, even if a dynamic evaluation of the sitting posture is achieved, data are used only to classify postures and not to evaluate the dynamic behavior of a subject in different conditions.

In a previous work [21], we equipped an office chair with textile sensors that allowed us to recognize 8 different sitting positions. We experimented a limitation since the smart chair allows only the detection of specific positions and not to monitor their evolution in time.

To evaluate the dynamic features of the seated position, we took inspiration from the use of force plates in posturography: in that domain, a three-component force plate is generally used to record over time where the Center of Pressure (COP) is located, by measuring and combining the vertical force component and the two torque components applied on it [22]. The COP is defined as the application point of the ground reaction force, and, in upright stance, it sways dynamically around an equilibrium point even in absence of external disturbances [23], a phenomenon that is generally denoted as postural sway. Postural sway is controlled by the Central Nervous System (CNS) in an autonomous way, and it is strictly related to the human capability of standing [24]. Human standing position is influenced by many disturbing factors (external, such as audio or visual stimuli, or internal, such as respiration or cardiac activity [25,26]) that are continuously compensated by the CNS.

Similarly, while seated, the human body is subject to a number of disturbances and, also in this condition, the CNS modulates the activity of muscles to maintain the equilibrium of the upper body segments (e.g., upper trunk, head, upper limbs) [27]. Correspondingly, in a seated position it is possible to determine where the Upper body Center of Pressure (UCOP) is located over a period of time, in order to evaluate, for example, if, in the presence of different external stimuli, or during task execution, a different way of swinging can be identified and to what it can be associated.

In both cases the equilibrium can be affected by different cognitive load levels of the task that a subject is performing. Different levels of cognitive load can be associated with variations of the electroencephalogram (EEG) signal [28]. In [29] the authors show that the EEG signal can be used to monitor different levels of stress. Moreover, it is known that an increase of cognitive load induces increasing levels of stress [30].

Among the techniques used to increase the cognitive load, the analysis of the EEG signals has proven that the Stroop Test activates brain areas related to attention [31]. Since this test can be a valuable tool to induce different cognitive loads on subjects, it has been used in the experiments presented in this work and it will be detailed in the following.

Anyway, EEG-based techniques require complex setup to record this type of signals. For this reason, EEG is not the most convenient means to monitor the level of stress in common daily life activities, such as in workplaces. Among the possible alternatives, it has been demonstrated that both eye movements and postural sway can be associated to different levels of cognitive involvement: in [32], 16 volunteers were asked to perform visual tasks while standing and they highlight the presence of a synergic relation between recorded eye and body movements for high precision tasks; moreover, even if some categories of trained people (e.g., activities that requires more equilibrium such as dancing) are in general more stable, everybody has a tendency to swing more when a demanding task is required [33], and this evidence makes space for the possibility to monitor cognitive load through the variations in postural sway. Following along this line, in [34], a Nintendo Wii balance board was selected to analyze the postural sway of older adults with no cognitive disability while performing predefined tasks in a home environment. In this case also, postural sway has been correlated to the cognitive status of the examined subjects.

In this work, the seated postural sway was analyzed using an innovative instrumented chair able to collect in a non-invasive way the instantaneous position of the UCOP. To test its validity, we asked subjects to perform a task sequence with increasing levels of cognitive engagement. As demonstrated in [21], increasing levels of cognitive engagemen<sup>t</sup> modify the posture that, starting from a relaxed seated condition will reach a stressed one, but up to now this was not quantified by the amount of seated postural sway associated with the observed modifications in posture.

### **2. Materials and Methods**

### *2.1. Instrumented Chair Design*

To evaluate the seated postural sway, a new instrumented chair has been designed and realized starting from previous experiences [21,35,36], where pressure sensors have been used to determine static postures of the users. In this work, an office chair was equipped with a set of four force sensors placed under its Load Plane (LP, i.e., where the pelvis loads up the chair). This set up was used to extract the instantaneous position of the UCOP mediolateral and anteroposterior coordinates (i.e., XUCOP and YUCOP), under the hypothesis that the remaining body segments (thighs, legs, foot) do not concur to loading the seat.

In analogy to posturography in an upright stance, the required dynamic components to calculate the UCOP coordinates are: the resultant vertical force applied on LP Fz, that is the force component acting along the perpendicular Z axis; and the two torques Mx and My applied around the orthogonal axes identified on the load plane, identified as X and Y (Figure 1).

**Figure 1.** Scheme of the instrumented chair load plane: The reference system for the dynamic components are identified by (x,y,z) axes, while the load cells positions are identified by the {A,B,C,D} markers.

Considering that Mx and My are defined as the vector product of Fz and the distance of its point of application on LP from each axis, the values of the UCOP coordinates, XUCOP and YUCOP, can be obtained as:

$$\chi\_{\rm UCOP} = \frac{\mathbf{M\_y}}{\mathbf{F\_x}}; \ Y\_{\rm UCOP} = -\frac{\mathbf{M\_x}}{\mathbf{F\_x}}.\tag{1}$$

To evaluate these three dynamic components, four load cells can be inserted in the positions {A,B,C,D} of the LP (Figure 1) and the four force components {F A, FB, FC, FD} can be measured. Consequently, Fz can be obtained as:

$$\mathbf{F\_z = F\_A + F\_B + F\_C + F\_D} \tag{2}$$

Each load cell produces a voltage output VP that in linear conditions results:

$$\mathbf{F}\_{\rm P} = \mathbf{k}\_{\rm P} \mathbf{V}\_{\rm P} \tag{3}$$

where P = {A,B,C,D} represents the position and kP is a proportionality constant.

If FZ is applied in the center of the LP (i.e., XUCOP = 0, YUCOP = 0) the four load cells are equally loaded and the torques applied around the X and Y axes are equal to zero, so it results:

$$\mathbf{k}\_{\rm A} \mathbf{V}\_{\rm A} = \mathbf{k}\_{\rm B} \mathbf{V}\_{\rm B} = \mathbf{k}\_{\rm C} \mathbf{V}\_{\rm C} = \mathbf{k}\_{\rm D} \mathbf{V}\_{\rm D} = 0.25 \times \mathbf{F}\_{\rm z}.\tag{4}$$

Considering that four load cells with the same features are used (thus the proportionality constant is the same for all the load cells), the previous equation can be approximated by:

$$\mathbf{F\_z = K\_z(V\_A + V\_B + V\_C + V\_D) = K\_z V\_{Fz}} \tag{5}$$

with KZ the common constant of proportionality for the Fz measurement.

When FZ is applied on a point that does not lie on one or both axes, one or both torque components are applied on the LP.

For example, when Fz is applied in a generic point on the x axis different from zero, a Mx component results on the LP; in this case the four load cells are loaded in a different way and it results that:

$$\mathbf{M}\_{\mathbf{x}} = \frac{1}{2} [ (\mathbf{k}\_{\mathbf{B}} \mathbf{V}\_{\mathbf{B}} + \mathbf{k}\_{\mathbf{C}} \mathbf{V}\_{\mathbf{C}}) - (\mathbf{k}\_{\mathbf{A}} \mathbf{V}\_{\mathbf{A}} + \mathbf{k}\_{\mathbf{D}} \mathbf{V}\_{\mathbf{D}}) ] \tag{6}$$

where *l* is the distance between A and B (or between C and D).

This equation represents the sum of each torque contribution given by the force reactions, due to Fz solicitation, applied in the four P positions. Since the hypothesis of using load cells with the same features still holds, the previous equation can be approximated by:

$$\mathbf{M}\_{\mathbf{k}} = \frac{\mathbf{lK}\_{\mathbf{z}}}{2} [ (\mathbf{V}\_{\mathbf{B}} + \mathbf{V}\_{\mathbf{C}}) - (\mathbf{V}\_{\mathbf{A}} + \mathbf{V}\_{\mathbf{D}}) ] = \mathbf{K}\_{\mathbf{k}} [ (\mathbf{V}\_{\mathbf{B}} + \mathbf{V}\_{\mathbf{C}}) - (\mathbf{V}\_{\mathbf{A}} + \mathbf{V}\_{\mathbf{D}}) ] = \mathbf{K}\_{\mathbf{x}} \mathbf{V}\_{\mathbf{Mx}} \tag{7}$$

with Ky a general constant of proportionality.

> With similar considerations, it is possible to write that:

$$\mathbf{M}\_{\mathbf{y}} = \mathbf{K}\_{\mathbf{y}}[(\mathbf{V}\_{\mathbf{C}} + \mathbf{V}\_{\mathbf{D}}) - (\mathbf{V}\_{\mathbf{A}} + \mathbf{V}\_{\mathbf{B}})] = \mathbf{K}\_{\mathbf{y}} \mathbf{V}\_{\mathbf{M} \mathbf{y}}.\tag{8}$$

It is then possible to measure Fz, MX and My if the three parameters {Kx, Ky, Kz} and the four voltage values {V A, VB, VC, VD} are known. This computation allows to compute the UCOP coordinates, XUCOP and YUCOP.

Each force component can be measured by a load cell and, after the signals are acquired, the mechanical quantities values can be calculated combining the digitalized data. These equations are valid in ideal conditions, where the cross-talk e ffect among channels (i.e., the influence of a specific load on all output channels, given by multiple factors) is neglected. In real conditions, every mechanical quantity is obtained taking in account cross-talk e ffects and properly modifying the given equations with a corrective factor; this is usually achieved by a calibration procedure that will be described in the following.

Using a normal office chair, four commercial load cells were placed in the four corners of its seat, to realize an instrumented system, where an LP can be identified, with the features described above. A custom frame was realized and used to partially replace the chair frame to obtain four areas of where to place the load cells (Figure 2). The custom frame was designed in order not to flex during dynamic solicitation, and not to affect the measures performed with the load cells.

**Figure 2.** Custom frame realized to house the load cells: (**a**) first part of the new frame fixed on the chair structure; (**b**) second part of the new frame fixed under the seat; (**c**) load cells housing.

The load cells used in this project are the FX1901 class (Measurement Specialties Inc., TE Connectivity Group, USA), while the specific used model (FX1901-0001-0100-L) is a 1% load cell device with full scale ranges of 100lb compression (about 45kg). These devices, specifically designed for force sensing in "smart" consumer and medical products, use micro-machined piezoresistive strain gauges, showing a ratiometric span of 20 mV/V.

To place the load cells under the LP, a specific adaptor was designed and realized by means of a 3D printing process. A Stratasys Objet30 Prime was used: this machine allows polyJet 3D printing that allows the realization of high-resolution components by jetting microscopic layers of liquid photopolymer onto a build tray and instantly curing them with UV light. This accuracy in realization, comparable with a high accuracy machining of metal alloy, was necessary to couple the 4 load cells with the flat surface of the metal frame where they have been housed. In Figure 3, one of the realized adaptors is shown: the load cell is fixed to the lower part of the adaptor and is covered by a two-piece top part. This part presents a cylindrical element that is in contact with the load-sensitive part of the load cell and with the top part of the custom chair frame, thus transmitting directly to the load cell the force applied on the LP.

Each load cell, as mentioned above, was realized using strain gauges that are assembled in a full Wheatstone bridge configuration. As mentioned in its datasheet, a 4-wire connection is provided: 2 wires are used to supply the Wheatstone bridge {+Vin, −Vin}, while 2 wires are used to measure its outputs {+Vout, −Vout}.

The four load cells were driven independently using four instrumentation amplifiers, INA125 (Texas Instruments inc., USA). It is a high-accuracy instrumentation amplifier with a precision voltage reference used to provide a complete bridge excitation and that can receive and amplify differentially the bridge output. The gain was set using the dedicated single external resistor pin, using the datasheet information (selectable gain from 4 to 10,000) in order to best fit the voltage range of the adopted A/D converter. This last operation was performed using an Arduino Uno (Arduino cc) board, that through an ATmega328P microcontroller provided the necessary function to acquire

signals. A specific firmware was realized to acquire from four input channels of the Arduino board the four INA125 output analog signals with a 100 Hz sampling frequency.

**Figure 3.** Load cells housing adaptors: (**a**) open adaptors; (**b**) closed adaptor with enclosed load cell: the central cylindrical element is in contact with the load-sensitive part of the load cell.

The AD converter was managed by using a custom interface realized with Labview (National Instruments, USA) that allows the connection with the Arduino board via USB. The designed and realized Labview panel (i.e., Virtual Instrument, VI), allows the serial port connection to receive the digitalized data that are converted from bit levels to mechanical quantities using proper calibration coefficients. Moreover, the VI calculates in real time the UCOP coordinates and all data (i.e., Fz, Mx and My together with XUCOP YUCOP) are saved in a file for further elaboration.

The mechanical quantities in real conditions, where cross-talk effects are present, are obtained from the acquired voltage values according to the following equations:

$$\begin{cases} \begin{aligned} \mathbf{F}\_{\mathbf{z}} &= a\_{11} \mathbf{V}\_{\mathbf{F}\mathbf{z}} + a\_{12} \mathbf{V}\_{\mathbf{M}\mathbf{x}} + a\_{13} \mathbf{V}\_{\mathbf{M}\mathbf{y}}\\ \mathbf{M}\_{\mathbf{x}} &= a\_{21} \mathbf{V}\_{\mathbf{F}\mathbf{z}} + a\_{22} \mathbf{V}\_{\mathbf{M}\mathbf{x}} + a\_{23} \mathbf{V}\_{\mathbf{M}\mathbf{y}}\\ \mathbf{M}\_{\mathbf{y}} &= a\_{31} \mathbf{V}\_{\mathbf{F}\mathbf{z}} + a\_{32} \mathbf{V}\_{\mathbf{M}\mathbf{x}} + a\_{33} \mathbf{V}\_{\mathbf{M}\mathbf{y}} \end{aligned} & \Rightarrow \begin{pmatrix} \mathbf{F}\_{\mathbf{z}}\\ \mathbf{M}\_{\mathbf{x}}\\ \mathbf{M}\_{\mathbf{y}} \end{pmatrix} = \begin{pmatrix} a\_{11} & a\_{12} & a\_{13} \\\ a\_{21} & a\_{22} & a\_{23} \\\ a\_{31} & a\_{32} & a\_{33} \end{pmatrix} \begin{pmatrix} \mathbf{V}\_{\mathbf{F}\mathbf{z}}\\ \mathbf{V}\_{\mathbf{M}\mathbf{x}}\\ \mathbf{V}\_{\mathbf{M}\mathbf{y}} \end{pmatrix} \end{cases} \tag{9}$$

with ⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝ *a*11 *a*22 *a*33 ⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠ = ⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝ Kz Kx Ky ⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠ and *aij* a generic calibration coefficient, constituting the calibration matrix,

that is used to take into account the cross-talk effect. Since load cells' primary transducers work in their linear field, the calibration coefficients can be considered constant in the measurement range of the load cells.

Calibration coefficients have been obtained by positioning a graduate flat surface on the chair LP (Figure 4). The graduate surface has specific reference points that allow the application of controlled loads on the chair LP; as an example, by using known loads it is possible to apply only the Fz component or specific Mx and My, since the equidistant orthogonal axes from load cells couples are identified. Thus, considering three different load conditions, and reading the correspondent voltage output, it is possible to apply three times Equations (9) to obtain the calibration coefficients.

**Figure 4.** Load cells calibration setup performed using a graduate reference surface positioned on the chair LP and known loads.
