Entropic Characterization of Multiple Physiological Responses with Statistical Process Control Charts

Several studies have been conducted in the past to examine the relationship among the elements of stress, nervous system, and physiological processes [1]. It has been well established that the physiological signals provide a quantitative measure of stress depending on the nature of the imposed stressors [2]. The complexity of the human physiological stress responses to any external stimuli or a combination of stressors poses a major challenge to better understand the consequences of stressful events in life. In general, the impact of both acute and chronic stressors on human physiological health is not clearly understood at the present time. Despite numerous studies in the past, there is no composite quantitative measure of physiological stress response that could be used to monitor human physiological health. The motivation behind this study is to overcome this limitation by combining multiple physiological responses in terms of entropy change (∆S) using Maxwell relations from thermodynamics to provide a quantitative measure of stress. In the fields of quality engineering, statistical process control charts (SPC) are routinely used to track any process quality using key performance indicators (KPIs) [3, 4]. The physiological entropy change utilized as a KPI for monitoring stress level could be used in SPC charts similar to manufacturing. This methodology could help healthcare professional in the real-time diagnosis and subsequent treatment of health issues.

Aoki [5, 6] has examined human thermoregulation using entropy generation with the second law of thermodynamics. Bejan [7] has developed constructal law relations to explain the physiological dynamics of breathing and heart beating. However, these previous studies do not use thermodynamic Maxwell relations and do not include multiple physiological responses. The present study is unique that it combines multiple physiological responses in a meaningful manner using Maxwell relations to provide a quantitative measure of stress.

The law of psychophysics states that the psyche itself cannot be measured directly but it can be interpreted in terms of changes in physical variables [8]. Using a similar logic, the present study is based on the thermodynamics-based premise that entropy itself cannot be measured directly but it can be expressed in terms of changes in multiple physical variables such as pressure, volume, temperature, length, and tension [9, 10]. The changes in multiple physiological variables are mapped to that of physical system and are expressed in terms of physiological entropy change using Maxwell relations by Boregowda et al. [11-13]. The earlier studies conducted by Boregowda et al. [11] used time-series data but it did not address the use of entropy change as a key performance indicator in statistical process control charts. The NASA study involved the collection of five physiological signals including blood pressure, heart rate, skin temperature, electromyogram, and electrodermal response as described in the methodology section. The results and discussion begin with an illustrative example of entropy change calculation for subject number one followed by the demonstration of a statistical process control chart for the same human subject for the sake of brevity. However, the variation in entropy change in seven subjects is presented graphically in terms of mean, upper control limit (UCL), and lower control limit (LCL) values for all seven subjects. The single-factor ANOVA test is conducted on mean, UCL, and LCL values of entropy change. The results indicate a statistically significant difference in physiological entropy change in seven subjects. The primary goal of this study was to create a pathway for deeper physiological investigation of entropy change as a quantifiable key performance indicator for monitoring of whole physiological health status and stress level. Furthermore, the physiological entropy change metric provides a holistic measure of physiological stress that could be integrated into health monitoring systems for clinical decision-making. The methodology and formulation of physiological entropy change are presented in the sections 2 and 3 while the results in section 4 demonstrate the utility of the entropy change as a KPI for monitoring stress level and health status. The results indicate that the entropy change as a KPI provides a single summative number that could be utilized as a metric for quantifying health status and stress that is sorely missing in the literature.  

Entropy has been established as a measure of disorder in any system in the universe [9, 10]. Specifically, entropy generation as a measure of disorder is a kind of global measure that specifies how violent motions and reactions are occurring in nature. Hence, the entropy generation in the human physiological system shows the extent of activity within the body as a whole; thus, the entropy generation is a significant quantity that characterizes the human body from both thermodynamic and holistic (i.e., considering a human body as a whole) viewpoints [5, 6]. Thermodynamics with its biological origins [14], is particularly well-suited to study human physiological systems behavior [14-19]. It has been hypothesized by Bridgman [15] that the laws of thermodynamics are intrinsically positioned to model the physiological behavior of living systems. The state of the physiological system without an energetically significant measurement such as entropy generation would lead to a violation of the second law of thermodynamics [16, 17].

The physiological entropy-change, ΔS, derived from the Maxwell relations, is provided in detail in references [11-13]. It is based on the premise that entropy itself cannot be measured but can be interpreted in terms of measurable physical variables using Maxwell relations [9, 10]. The logic of Maxwell relations is consistent with the laws of psychophysics that psyche cannot be measured but can be interpreted in terms of physical variables, which in this study are the measurable peripheral physiological responses. It follows that the entropy-change in the human physiological system, (ΔS)₁, characterized by BP, HR, and ST is given by:

$(\Delta S)_1=\frac{\Delta B P \times \Delta H R}{\Delta S T}$                           (1）

where,

$\begin{gathered}\Delta B P=\left(B P_{\text {Task }}-B P_0\right), m m H g \\ \Delta H R=\left(H R_{\text {Task }}-H R_0\right), b p m \\ \Delta S T=\left(S T_{T a s k}-S T_0\right), K\end{gathered}$

Similarly, the entropy-change in the human physiological subsystem, (ΔS)₂, characterized by EMG, EDA, and ST is given by:

$(\Delta S)_2=\frac{\Delta E M G \times \Delta \mathrm{EDA}}{\Delta S T}$                                （2）

where,

$\begin{gathered}\Delta E M G=\left(E M G_{T a s k}-E M G_0\right), m V \\ \Delta E D A=\left(E D A_{T a s k}-E D A_0\right), \mu m h o \\ \Delta S T=\left(S T_{T a s k}-S T_0\right), K\end{gathered}$     

It is noticeable that the skin temperature is present in the denominator of all the above entropy change equations. In thermodynamic terms, it acts as a temperature at the boundary of the thermodynamic system and provides a physiological reflection of emotional response [2]. A single physiological indicator does not provide much information about the holistic nature of human physiology. This is due to the psychophysiological concepts such as stimulus response (SR) specificity, organ response (OR) specificity, individual response (IR) specificity, and autonomic balance that make the human physiological response to any stimuli a complex phenomenon [2]. These realities reflect the fact that the different individuals react differently to different stimuli via different organ systems. For instance, a person might exhibit higher blood pressure to a traumatic event or a memory of it while another person might respond with intense facial tension with higher electromyogram. The single physiological indicators provide a narrower knowledge of the physiological stress response. It is only by recognizing the interaction among various physiological responses to any stressor stimuli that one could build better physiological models, which is one of the objectives of this study.

Most of the past studies have focused on single physiological indicator or subjective questionnaires or performance or behavioral actions to interpret stress. These past metrics have served the purpose of limited research investigations and narrower applications but they do not provide any scientific method to quantify stress in terms of single number. Furthermore, there has been no meaningful metric that combines multiple physiological responses to provide a quantitative measure of stress in terms of a single number. The present study was conducted to fill this major gap to assess human physiology and interpret stress response.

The study involved collection of five physiological signals from seven subjects in a NASA pilot study who performed a mission-critical monitoring cognitive task. Five physiological signals included blood pressure, heart rate, finger skin temperature, electromyogram, and electrodermal response. These five signals were combined using Maxwell relations to provide a quantitative measure of entropy change that was used as a KPI represented in statistical process control charts. The results demonstrate critical psychophysiological concepts such as individual response (IR) specificity, organ response (OR) specificity, and stimulus response (IR) specificity [2]. In other words, the stress response to a particular stimulus varies from individual to individual while within the same individual, there is variation in how different organ systems respond to the same stimuli. The single factor ANOVA indicate statistically significant difference in individual stress response warranting further physiological investigation.

The present study with limited data demonstrates the potential utility of entropy change as a key performance indictor (KPI) that can be used to provide a holistic measure of human physiological stress response that could be developed into a clinical decision-making tool for medical diagnosis, preventive health treatments, and human operator stress monitoring in mission-critical applications. To achieve this goal, a large-scale study involving collection of multiple physiological data from large number of subjects needs to be conducted. The results from this type of study needs to be validated and verified for clinical applications. One of the futuristic goals is to use wearable sensors to track multiple physiological stress responses to examine the impact of stressors in real-time work and living environments for preventive health management.