Research Article Measuring Entropy Change in a …downloads.hindawi.com/archive/2016/4932710.pdfResearch Article Measuring Entropy Change in a Human Physiological System SatishBoregowda,

Research ArticleMeasuring Entropy Change in a Human Physiological System

Satish Boregowda,1 Rod Handy,2 Darrah Sleeth,2 and Andrew Merryweather3

1School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA2Department of Family & Preventive Medicine, University of Utah, Salt Lake City, UT 84108, USA3Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84108, USA

Correspondence should be addressed to Rod Handy; [email protected]

Received 11 November 2015; Revised 2 January 2016; Accepted 4 January 2016

Academic Editor: Felix Sharipov

Copyright 2016 Satish Boregowda et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

The paper presents a novel approach involving the use of Maxwell relations to combine multiple physiological measures to providea measure of entropy change. The physiological measures included blood pressure (BP), heart rate (HR), skin temperature (ST),electromyogram (EMG), and electrodermal response (EDR).Themultiple time-series physiological data were collected from eightsubjects in an experimental pilot study conducted at the Human Engineering Laboratory of NASA Langley Research Center. Themethodology included data collection during a relaxation period of eighteen minutes followed by a sixty-minute cognitive task.Two types of entropy change were computed: (a) entropy change (BP) due to blood pressure, heart rate, and skin temperatureand (b) entropy change (EMG) due to electromyogram, electrodermal response, and skin temperature. The results demonstratethat entropy change provides a valuable composite measure of individual physiological response to various stressors that could bevaluable in the areas of medical research, diagnosis, and clinical practice.

1. Introduction

Earlier work done by several researchers has established thefact that human life processes are indeed thermodynamic innature and hence thermodynamic laws can be used to modelhuman physiology. It has been hypothesized by Bridgman [1]that the laws of thermodynamics are intrinsic to nature andlife and are thuswell positioned to characterize the physiolog-ical behavior of living systems. Aoki [2, 3] examined humanthermoregulation bymeasuring entropy flow and productionin basal and exercising conditions but did not utilizeMaxwellrelations to include other physiological responses. The semi-nal work done in the areas of biological thermodynamics byMorowitz [4, 5] does not show any application of Maxwellrelations tomodel human physiology. Furthermore, the workdone by Garby and Larsen [6] and Jou and Llebot [7]addresses mass, energy, and entropy balance of open livingsystems but not Maxwell relations. However, the detaileddevelopment and preliminary verification of physiologicalentropy change using Maxwell relations have been presentedby Boregowda et al. [8, 9] and are reproduced in Appendixfor the convenience of the readers. The present study utilizes

time-series data collected during a cognitive task to validateand verify entropy change metrics representing two humanphysiological subsystems. For the convenience of the readers,the detailed development of physiological entropy changeusing Maxwell relations is presented in Appendix of thispaper.Thefirst one combines changes in bloodpressure, heartrate, and skin temperature to provide a BP-based entropychange (BP). The second one combines changes in elec-tromyogram, electrodermal response, and skin temperatureto provide an EMG-based entropy change (EMG).

2. Modeling and Formulation

2.1. Entropy Change (BP: Blood Pressure, Heart Rate, andSkin Temperature). Let us first consider the human phys-iological subsystem characterized by blood pressure (BP),heart rate (HR), and skin temperature (ST) as a closedthermodynamic system. For this system, the work done bythe system is given by [10]

= = BP (HR) , (1)

Hindawi Publishing CorporationJournal of ermodynamicsVolume 2016, Article ID 4932710, 8 pageshttp://dx.doi.org/10.1155/2016/4932710

2 Journal of Thermodynamics

where is pressure, BP is blood pressure (mmHg), isvolume, and HR is heart rate (beats/minute).

The heart rate is an indirect measure of stroke volumeof blood in the heart region and is, thus, used in the placeof stroke volume. Please note that heart rate (in beats perminute) is equal to cardiac output (mL/min) divided bystroke volume (mL/beat). The ratio of partial changes intwo physiological variables is accompanied by constancy inthe third variable, as this is the basis of Maxwell relations.For example, when there is a partial change in heart ratewith respect to partial change in entropy, the mean arterialpressure remains constant. As shown in Appendix, thethermodynamic potential is derived as shown starting withHelmholtzs potential ( = ) and arriving with thefollowing property relation:

= BP (HR) (ST) . (2)The following Maxwell relation is obtained by invoking theexactness condition to the above property relation (2):

(BPST) = (HR)T . (3)

The partial derivative is approximated to form a modifiedMaxwell relation that is used in the present experimentalstudy to compute the physiological entropy change resultingfrom changes in blood pressure (BP), heart rate (HR), andskin temperature (ST):

(BPST)HR= (BPHR)ST ,

BP = BP HRST .(4)

The skin temperature (ST) in the denominator acts as atemperature at the boundary of the closed thermodynamicsystem and provides a physiological reflection of emotionalresponse. If one were to consider either internal energy or theGibbs function to define human physiological function, thenone would get a negative sign preceding the entropy change(BP). The deviation from the relaxed state may be positiveor negative depending on the imposed external stressor andthe internal physiological condition.

2.2. Entropy Change (EMG: Electromyogram, ElectrodermalResponse, and Skin Temperature). Let us consider the humanphysiological subsystem characterized by electromyogram(EMG), electrodermal response (EDR), and skin temperature(ST) as a closed thermodynamic system. For this system, thework done by the system is given by

= = EMG (EDR) , (5)where is tension, EMG is facial electromyogram (mV), islength, and EDR is electrodermal response (mV).

In this regard, the elements of a human physiologicalsubsystem system are considered as equivalent to a conduct-ing wire with as tension and as the length. The facialelectromyogram (EMG) has been used in medical research

and clinical practice as a measure of tension in facial muscles[11]. As a result of tension in muscles or nerves, the outersurface of the skin responds by expanding or contractingin terms of changes called electrodermal response (EDR).The skin temperature (ST) represents the thermal responseto tension. The thermodynamic potential is again derived,starting with Helmholtzs potential ( = ) arriving atthe following property relation:

= EMG (EDR) (ST) . (6)The following Maxwell relation is obtained by invoking theexactness condition to the above property relation (2):

(EMGST )EDR = (EDR)ST . (7)

The partial derivative is approximated to form a modifiedMaxwell relation that is used in the present experimentalstudy to compute the physiological entropy change resultingfrom changes in blood pressure (BP), heart rate (HR), andskin temperature (ST):

(EMGST

)EDR= (EMGEDR )ST ,

EMG = EMG EDRST .(8)

As mentioned earlier, the use of either internal energy orthe Gibbs function would have resulted in a negative signpreceding the entropy change (). The deviation fromthe relaxed state may be positive or negative, depending onthe imposed external stressor and the internal physiologicalcondition. Specifically, physiological entropy is qualitativelydefined as a measure of disorder [12]. It is a kind of globalmeasure that specifies how violent motions and reactionsare occurring in nature. Hence, the entropy change in thehuman physiological system shows the extent of activitywithin the body as a whole; thus, the entropy change is asignificant quantity that characterizes the human body fromthermodynamic and holistic (i.e., considering a human bodyas a whole) viewpoints.

The human physiological entropy change could be con-sidered as a composite measure of change in the whole phys-iological state in response to any external stimuli or stressor.However, if a single physiological indicator alone, such as themean arterial pressure, can provide that information, thenwhy do we need this entropy change as a composite measureof physiological response? The answer is as follows: thephysiological concepts such as stimulus response (SR) speci-ficity, organ response (OR) specificity, individual responsespecificity, and autonomic balance make the human phys-iological response a complex phenomenon [11]. The singlephysiological indicators, in this regard, provide a very narrowrepresentation of the human physiological stress responsesystem. It is only by recognizing the interaction amonghuman subsystems in their response to any stressor stimulithat one could build a bettermodel of human physiology.Thisstudy makes an effort to reduce the physiological complexityin terms of a composite entropy change.

Journal of Thermodynamics 3

3. Methodology

3.1. Subjects. The data in the study were collected on eightsubjects (5 male, 3 female). These subjects completed a stan-dard psychophysiological stress profile procedure routinelyused for assessment in the Human Engineering Laboratoryat NASA Langley Research Center. The participants were allhealthy (i.e., without any major health problems).

3.2. Data Collection. The physiological data were collectedby a BioPac system via National Instrument LabView. Themultiple physiological responses were collected from eightsubjects who completed the 78-minute Physiological StressProfile and included the two following conditions.

Condition 1 (relaxation period). Subjects relaxed in a semire-clining positionwith eyes open for eighteenminutes listeningto a guided relaxation tape. The physiological stress responsedata were collected. These eighteen-minute time-series data,BP, HR, ST, EMG, and EDR, were averaged and usedin the physiological entropy change calculations as baselinedata points.

Condition 2 (task period). Subjects completed a series ofcognitive tasks presented by an oil refinery simulation pro-gram called Dexter. The primary goal of this simulationprogram was to examine the human physiological responseto activities that induce boredom, drift in attention, and othernegative effects on performance.The task lasted for sixtymin-utes and two data samples per minute were collected. Eachone of these physiological measuresBPTask, HRTask, STTask,EMGTask, and EDRTaskwas used in the calculations asshown in the next subsection.

3.3. Illustrative Example. Let us consider subject #1; theeighteen-minute time-series data is averaged to get thefollowing baseline values. Note that BP, and HR, areaveraged and used in the physiological entropy generationcalculations as baseline data points:

BP (mmHg): 118.74.HR (bpm): 68.49.ST (

F): 93.14.EMG (mV): 334.17.EDR (mho): 557.87.

Each one of the physiological measures, BPTask, HRTask,STTask, EMGTask, and EDRTask, from the time-series is used tofind the entropy change. Let us consider the values at the 5thminute during the task. A sample calculation of physiologicalentropy change at the 5th minute for subject #1 is shown asfollows:

BP = (BPTask BP) (HRTask HR)[(STTask ST) /1.8] ,

BP = (136.05 118.74) (81.97 68.49){(92.59 93.14) /1.8 }= 178.33mmHg bpm/K.

(9)

The EMG-based entropy change is calculated as follows:

EMG = (EMGTask EMG) (EDRTask EDR){[(STTask ST) /1.8] } ,

EMG = (335.25 334.17) (678.93 557.87){[(92.59 93.14) /1.8] }= 100.21mV mho/K.

(10)

Note the following:

(1) Divide temperature difference ST by 1.8 to get theunits in Kelvin (K).

(2) The factor is used to deal with zeros and smalltemperature difference that would cause huge entropychange numbers. In this case, = 1 since ST isnegative. If it is positive then = +1. This keeps themagnitude of the entropy change to within manage-able limits while keeping the direction of temperaturechange congruent.

The above sample calculations are done for the entire taskperiod of sixty minutes for each subject and repeated for allthe eight subjects as illustrated in the next section.

4. Results and Analysis

The baseline data were obtained by averaging the eighteen-minute relaxation period and are provided in Table 1 for theeight subjects. The BP and EMG results are presented inFigures 1 and 2.

Figures 1 and 2 quantitatively demonstrate keypsychophysiological important concepts such as stimulusresponse (SR) specificity, organ response (OR) specificity, andindividual (IR) response specificity [11]. For each subject, theresponse to the task varies within the sixty-minute period.For instance, in Figure 1, subject 4 shows normal variabilitywith BP throughout the task. This is a demonstrationof stimulus response (SR) specificity. In Figure 2, thesame subject #4 shows greater variability with EMG in thebeginning of the task while learning to settle down as the taskprogresses. This is a demonstration of organ response (OR)specificity in which the subject is exhibiting higher reactivityvia EMG and EDR combinations. Also, one can observe widevariations between individual subjects in both Figures 1 and 2,which demonstrates individual response (IR) specificity.Furthermore, the average entropy change value over a 60-minute time period was obtained for all eight subjects andshown graphically in Figure 3. It is observed that there is awide variation among the subjects in terms of average entropychange response to the task demonstrating interindividualdifferences. These results demonstrate the importance of athermodynamics-based approach to conducting any medicaland/or clinical research involving human subjects.

It is clear from the results shown in Figure 3 that subjectsshow greater reactivity via entropy change (EMG) induced


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Figure 1: Entropy change (BP) across eight subjects: 1, 6, and 7 show significantly different patterns of variations compared to others.

by EMG and EDR than that by entropy change (BP)induced by blood pressure and heart rate. Both have tem-perature change as commondenominators. Because of higherreactivity, EMG involving EMG and EDRmeasures need tobe included in any comprehensive medical stress studies.

5. Conclusion

The study was based on the premise that Maxwell relationscould be used to compute entropy change in terms of mea-surable physical variables. The experimental study involved


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Figure 2: Entropy change (EMG) across eight subjects: 2, 5, and 8 show significantly different patterns of variations while 7 exhibits a uniquepattern.

eight subjects and was conducted in the Human Engi-neering Laboratory at NASA Langley Research Center.The physiological variables were measured at two states,relaxed and stressor task.The average physiological measurestaken during relaxation were taken as the baseline values.

The physiological changes in blood pressure, heart rate, elec-tromyogram, electrodermal response, and skin temperaturefrom the reference (State 1) to stressor (State 2) were usedin the Maxwell relations obtaining entropy changes, BP,and EMG, respectively. The results validate and verify key


Table 1: Baseline values from the relaxation period for eight subjects.

Subjects BP (mmHg) HR (bpm) ST (F) EMG (mV) EDR (mho)

1 118.74 68.49 93.14 334.17 557.872 120.36 68.30 90.26 903.86 100.863 144.37 44.64 83.72 418.81 52.694 145.67 45.58 91.34 372.77 40.545 135.90 67.85 90.92 897.79 20.006 139.43 47.44 87.73 477.24 205.907 140.17 73.16 75.64 373.94 381.628 122.73 65.70 91.46 886.80 11.08

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Figure 3: Average entropy change response in eight subjects.

psychophysiological concepts such as individual response(IR) specificity, organ response (OR) specificity, and stimulusresponse (IR) specificity.

The main purpose of this study was to use a novelthermodynamics-based approach to provide quantitativeframework to assess human physiological stress responses.It is clear from the result that the modified Maxwell rela-tions indeed provide something valuable to the biomedicalengineering, medical, and health community, a quantitativemeasure of disorder or stress in human physiology. Theentropy change could be postulated as disorder (probability)and incorporated in Shannons entropy formulation [13] tolink physical and informational aspects of human physiology.As this is beyond the scope of this paper, it could be valuableto the biomedical engineering community to utilize thisconcept for future applications. This fundamental conceptcould also lead to development of noninvasive, wearablesensors in order to gain insight into the prevention of humanerrors and occupational injuries and diseases. Future effortswill target field applications of this methodology. Specifically,the researchers plan to evaluate its usability and merit inoccupational settings where workers are exposed to eitherphysical (e.g., extreme temperatures, radiation), chemical

Table 2: Human biothermal-fluid system.

Physical variables Biothermal-fluid systemPressure () Blood pressure (BP)Volume () Heart rate (HR)Temperature () Skin temperature (ST)Entropy () BP-based entropy (BP)

(e.g., particulate matter, organics solvents), or biologicalstressors (e.g., mold, fungi).

Appendix

A. Using Maxwell Relations to MeasureEntropy Change in Human Physiology

A.1. Derivation of BP for Human Biothermal-Fluid System.TheMaxwell relations were used to calculate entropy change(BP) in terms of measurable physical quantities such aspressure, volume, and temperature. An analogy between asimple physical piston-cylinder system and human physi-ological subsystem is conceptualized. The physical systemcharacterized by pressure (), volume (), and temperature() is mapped to that of a human biothermal-fluid system,blood pressure (BP), heart rate (HR), and skin temperature(ST), accordingly as shown in Table 2.

A.1.1. Assumptions. (a) Human subphysiological systemcharacterized by BP, HR, and ST is considered as a simpleclosed system from a macroscopic perspective for the pur-pose of this study. This makes it possible to apply Maxwellrelations to examine human physiology.

(b) Blood pressure (BP), heart rate (HR), and skintemperature (ST) are equivalent to pressure (), volume (),and temperature (), respectively, as shown in Table 2.

A.1.2. Analysis. Let us consider a variable that is a continu-ous function of and :

= (, ) . (A.1)


It is convenient to write the above equation in the followingform:

= + , (A.2)

where

= () ;

= () .(A.3)

If in (A.1), , , and are all point functions (i.e., quantitiesthat depend only on the state and are independent of thepath), the differentials are exact differentials. Therefore, inorder for (A.1) to be an exact differential equation, thefollowing condition must be satisfied:

( ) = ( ) . (A.4)

Equation (A.4) is called the exactness condition.Maxwell relations are derived from the property relations

of thermodynamic potentials by invoking the exactnesscondition. For a simple blood pressure-based human physio-logical subsystem, there are four thermodynamic potentials:

Internal Energy: BP = STBP BPHR, (A.5a)Enthalpy: BP = STBP +HRBP, (A.5b)

Helmholtz Function: BP = BPHR BPST, (A.5c)Gibbs Function: BP = HRBP BPST. (A.5d)

The followingMaxwell relations are obtained by invoking theexactness condition to the above four property relations:

( STHR)BP = (BPBP)HR , (A.6a)

(STBP)BP = (HRBP )BP , (A.6b)

(BPST)HR = (BPHR)BP , (A.6c)

(HRST )BP = (BPBP )ST . (A.6d)

The above-mentioned partial derivatives are approximated toform a modified set of Maxwell relations that are used in

Table 3: Human biothermal-electric system.

Physical variables Biothermal-electric systemTension () Electromyogram (EMG)Length () Electrodermal response (EDR)Temperature () Skin temperature (ST)Entropy () EMG-based entropy (EMG)

the present experimental study to compute the physiologicalentropy change:

( STHR)BP = (BPBP)HR , (A.7a)

(STBP) = (HRBP )BP , (A.7b)

(BPST)HR = (BPHR)BP , (A.7c)

(HRST )BP = (BPBP )ST . (A.7d)

Any of the above relations (A.7a)(A.7d) could be used toquantify BP, the human physiological entropy change.Using the Helmholtz function-based thermodynamic poten-tial, the entropy change is given by

BP = BP HRST . (A.8)

A.2. Derivation of EMG for Human Biothermal-Electric Sys-tem. Thephysical system characterized by tension (), length(), and temperature () is mapped to that of a humanbiothermal-electric system, electromyogram (EMG), electro-dermal response (EDR), and skin temperature (ST), accord-ingly as shown in Table 3.

A.2.1. Assumptions. (a) Human subphysiological systemcharacterized by EMG, EDR, and ST is considered as asimple closed system from a macroscopic perspective for thepurpose of this study.Thismakes it possible to applyMaxwellrelations to examine human physiology.

(b) Electromyogram (EMG), electrodermal response(EDR), and skin temperature (ST) are equivalent to tension(), length (), and temperature (ST), respectively.

A.2.2. Analysis. Maxwell relations are derived from the prop-erty relations of thermodynamic potentials by invoking theexactness condition. For a simple blood pressure-based


human physiological subsystem, there are four thermody-namic potentials:

Internal Energy: EMG= STEMG EMGEDR,

(A.9a)

Enthalpy: EMG = STEMG + EDREMG, (A.9b)Helmholtz Function: EMG= EMGEDR EMGST,

(A.9c)

Gibbs Function: EMG= EDREMG EMGST.

(A.9d)

The followingMaxwell relations are obtained by invoking theexactness condition to the above four property relations:

( STEDR)EMG = (EMGEMG )EDR , (A.10a)

( STEMG)EMG = (EDREMG)EMG , (A.10b)

(EMGST )EDR = (EMGEDR )EMG , (A.10c)

(EDRST )EMG = (EMGEMG)ST . (A.10d)

The modified set of Maxwell relations that are used in thepresent experimental study to compute the physiologicalentropy change are

( STEDR)EMG = (EMGEMG )EDR , (A.11a)

( STEMG)EMG = (EDREMG)EMG , (A.11b)

(EMGST )EDR = (EMGEDR )EMG , (A.11c)

(EDRST )EMG = (EMGEMG)ST . (A.11d)

Using the Helmholtz function-based thermodynamic poten-tial (A.11c), the entropy change is given by

EMG = EMG EDRST . (A.12)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

The authors wish to thank Dr. Alan Pope of NASA LangleyResearch Center for the initial support of this researchproject.

References

[1] P. W. Bridgman, The Nature of Thermodynamics, Harpers andRow, New York, NY, USA, 1961.

[2] I. Aoki, Entropy flow and entropy production in the humanbody in basal conditions, Journal ofTheoretical Biology, vol. 141,no. 1, pp. 1121, 1989.

[3] I. Aoki, Effects of exercise and chills on entropy production inhuman body, Journal of Theoretical Biology, vol. 145, no. 3, pp.421428, 1990.

[4] H. J. Morowitz, Entropy for Biologists, Academic Press, NewYork, NY, USA, 1970.

[5] H. J. Morowitz, Foundations of Bioenergetics, Academic Press,New York, NY, USA, 1978.

[6] L. Garby and P. S. Larsen, Bioenergetics: Its ThermodynamicFoundations, Cambridge University Press, Cambridge, UK,1995.

[7] D. Jou and J. E. Llebot, Introduction to the Thermodynamics ofBiological Processes, Prentice-Hall, Englewood Cliffs, NJ, USA,1990.

[8] S. C. Boregowda, S. N. Tiwari, S. K. Chaturvedi, and D. R.Redondo, Analysis and quantification of mental stress andfatigue usingMaxwell relations from thermodynamics, Journalof Human Ergology, vol. 26, no. 1, pp. 716, 1997.

[9] S. C. Boregowda and W. Karwowski, Modeling of humanphysiological stresses: a thermodynamics-based approach,Occupational Ergonomics, vol. 5, no. 4, pp. 235248, 2005.

[10] H. Callen,Thermodynamics and an Introduction toThermostat-ics, John Wiley & Sons, New York, NY, USA, 2nd edition, 1985.

[11] J. L. Andreassi, Psychophysiology: Human Behavior and Physio-logical Stress Response, Lawrence ErlbaumAssociates, Mahwah,NJ, USA, 4th edition, 2007.

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[13] C. E. Shannon, Amathematical theory of communication,TheBell System Technical Journal, vol. 27, no. 3, pp. 379423, 1948.

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Research Article Measuring Entropy Change in a …downloads.hindawi.com/archive/2016/4932710.pdfResearch Article Measuring Entropy Change in a Human Physiological System SatishBoregowda,