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A Statistical Analysis of Human Body Temperature. By: Dhanalakshmi Pantangi Praneetha Mukhatira Yaping Sun. Introduction: Normal Body temperature

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A Statistical Analysis of

Human Body Temperature


Dhanalakshmi Pantangi

Praneetha Mukhatira

Yaping Sun


Normal Body temperature

The normal core body temperature of a healthy, resting adult human being is stated to be at 98.6 degrees Fahrenheit or 37.0 degrees Celsius..

However, body temperature varies from person to person and is affected by factors such as

exercise, sleep, eating and drinking, and time of day.

The body's surface temperature rises and falls in response to the environment


Body temperature is maintained by the hypothalamus,

which constantly monitors blood temperature and activates mechanisms to compensate for changes.

When the body's surface temperature falls, the hypothalamus sends nerve impulses to the skin to stimulate shivering, which generates heat by muscle activity, and to restrict the blood vessels in the skin, which limits heat loss.

When the surface temperature rises, the hypothalamus stimulates the sweat glands in the skin to produce sweat and dilates the blood vessels in the skin to increase heat loss

. Because of the complexity of the human thermoregulatory system, there are an infinite number of components that may be included, or omitted depending on the primary use of the thermoregulatory model.

What is temperature?

Temperature refers to the degree of hotness or coldness of a body or environment.

Temperature may be defined as the condition of a body which determines the transfer of heat to or from other bodies.

Particularly, it is a manifestation of the average translational kinetic energy of the molecules of a substance due to heat agitation.

High temperature means that an object's constituent parts are moving around energetically. Absolute zero (0°K) is the point at which atomic and molecular motion stops; this temperature has not yet been achieved on earth.

Temperature scales:

  • F A H R E N H E I T (thermometric scale) :Named after Gabriel Daniel Fahrenheit (1686-1736),German physicist. Around 1714 Fahrenheit proposed that the freezing-point of water should be 32° (to avoid negative temperatures) and the boiling-point 212°.
  • R É A U M U R (thermometric scale) : Named after René-Antoine Ferchault de Réaumur (1683-1757), A French scientist.Réaumur proposed a new scale in 1730 that set the freezing-point at 0° and the boiling-point at 80°.
C E L S I U S (thermometric scale):Named after Anders Celsius (1701-1744), Swedish astronomer. The customary unit of temperature is the Centigrade degree, 1/100 of the difference between the temperature of melting ice and that of water boiling under standard atmospheric pressure. The Celsius temperature scale is a designation of the scale also known as the centigrade scale.
  • K E L V I N (absolute scale):Named after William Thomson, 1st Lord Kelvin (1824-1907), Scottish engineer, mathematician and physicist. Around 1862, Kelvin (in collaboration with J.P. Joule) proposed an absolute scale of temperature based on laws of heat rather than the on the freezing / boiling-points of water. From this work came the idea of absolute zero -- the temperature below which it is not possible to go (the point at which all molecular movement theoretically ceases). Absolute zero is 0°K (-273.15° Celsius).


  • The Liquid-in-glass Thermometer
  • Digital thermometers
  • Electronic thermometers
  • Infrared Ear Thermometers
  • Dot matrix or phase change thermometers

Importance of Units:

We take measurement units for granted as long as we don't have to convert to some other system. But converting units is always trouble.

NASA apparently lost the Mars Climate Orbiter spacecraft because of a problem converting units.

The familiar but over-exact 98.6 °F body temperature is also a units problem caused by preserving too many digits after converting. ." Different systems of units are so human, and so subject to human error. All modern temperature scales are based on measuring two points on a scale and extrapolating the rest..

The German physician Carl Reinhold August Wunderlich (1815 - 1877) made the original study of normal body temperature in the 1800s by doing a statistical study of thousands of people in Europe.

He was one of the first to describe fever as a symptom, not a disease by itself. He averaged his results to 37° Celsius, rounded to the nearest degree. But +/- 0.5 °C, is nearly a full degree Fahrenheit after converting by the formula °F = (9/5) °C + 32


Medical Service, Veterans Affairs Medical Center, Baltimore.

To evaluate critically Carl Wunderlich's axioms on clinical thermometry A critical appraisal of 98.6 degrees F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich.


Oral temperatures were measured one to four times daily for 3 consecutive days using an electronic digital thermometer .Taken from hundred forty-eight healthy men and women aged 18 through 40 years.

RESULTS--Our findings conflicted with Wunderlich's in that 36.8 degrees C (98.2 degrees F) rather than 37.0 degrees C (98.6 degrees F) was the mean oral temperature of our subjects; 37.7 degrees C (99.9 degrees F) rather than 38.0 degrees C (100.4 degrees F) was the upper limit of the normal temperature range; maximum temperatures, like mean temperatures, varied with time of day; and men and women exhibited comparable thermal variability.); women had slightly higher normal temperatures than men; and there was a trend toward higher temperatures among black than among white subjects.

CONCLUSIONS--Thirty-seven degrees centigrade (98.6 degrees F) should be abandoned as a concept relevant to clinical thermometry; 37.2 degrees C (98.9 degrees F) in the early morning and 37.7 degrees C (99.9 degrees F) overall should be regarded as the upper limit of the normal oral temperature range in healthy adults aged 40 years or younger.


The external heat transfer mechanisms are radiation, conduction and convection and evaporation of perspiration

The process is far more than the passive operation of these heat transfer mechanisms,

however. The body takes a very active role in temperature regulation.

The temperature of the body is regulated by neural feedback mechanisms which operate primarily through the hypothalamus.

The hypothalamus contains not only the control mechanisms, but also the key temperature sensors. Under control of these mechanisms, sweating begins almost precisely at a skin temperature of 36.8°C and increases rapidly as the skin temperature rises above this value.

Temperature Regulation of the Human Body

Body heat is dynamic, always changing, always moving across tissue boundaries.  Heat transfer occurs when there is a difference in heat content of adjacent areas. We call the sum of the differences between one area and another "gradient".  So what we are actually measuring when we measure body temperature is energy in motion in search of equilibrium from warmer to cooler.  Heat transfers in four ways as currently identified:
  • radiation........................through space without contact
  • convection.....................through air or liquid as contact medium
  • conduction....................through objects by direct contact
  • evaporation....................through liquid then to air

An equation for the body heat balance can be written as M ± W = ± R ± C ± E ± S [W/m²] where M is the rate at which thermal energy is produced by the body through metabolic processes, W is the rate of work produced by or on the body, R is the rate of radiant heat exchange with the surroundings, C is the rate of convective heat exchange with the surroundings, E is the rate of heat loss due to evaporation of body water, and S is the rate of heat storage in the body. Numerous studies have confirmed that in many species, an absorbed dose of microwave energy equivalent to the resting metabolic heat production elevates the deep body temperature of the animal by 1 degree or more. S should ideally be close to zero in order to prevent body temperature changes


Heat Losses :

We earlier defined the thermoregulatory model.

We modeled a person exercising on a level treadmill. We will assume that the resultant heat loss (wastage) is a parabolic function of speed, with a value of 11.2 Cal / min at a speed of 9 kmph.

We will further assume that y skin temperature varies parabolically from 28.2 C at an ambient temperature of 9.5 C to 37.2 C at an ambient temperature of 35 C.

Finally, we assume that you do not sweat when the ambient temperature is below 30 C and that above 30 C the rate of sweat is proportional to the amount by which your skin temperature exceeds 30 C.

These assumptions are based on studies on medical students. We will supplement them with an estimate of the amount of water vapor exhausted during respiration which is proportional to the rate of exercise.

Since the net heat loss or gain is a function of three variables (ambient temperature, rate of walking and wind speed), we have to analyze a three dimensional field.


This example shows the waste heat in red, evaporative losses in blue, convective losses in green and conductive and radiative losses in black, all as a function of ambient temperature for a given exercise level (6 km/hr) and wind velocity (5 m/s).

Abnormalities of Temparature causes following effects to the Body:
  • Maladies: There is a danger to life should the bodytemperature drop and remain below 95 degrees Fahrenheit (35 degrees Celsius) or rise and remain at or above 106 degrees Fahrenheit (41 degrees Celsius).
  • Fever: Increased Temperature of Body Cells (Pyrexia) Pyrexia, commonly known as fever, increases the cellular metabolic rate. It is one of the body's defense mechanisms against bacterial and viral infections.
  • Hyperthermia:Hyperthermia is not the same as fever.  It occurs when the body's temperature is exceeded without the hypothalamus altering the set point.  This can occur with excessive physical exertion or exposure to high temperatures and in response to certain medications, including, but not limited to, some anesthetic agents in persons prone to malignant hyperthermia.  Hyperthermia should be considered potentially life threatening.
  • Wilson's Syndrome:Wilson's Syndrome is chronic low body temperature. It may be genetic, triggered by stress or inactivity, as well as diet and starvation.
  • Hypothermia (Lowered Body Temperature):The body generates heat through metabolic processes that can be maximized with involuntary shivering to roughly five times the basal level (up to 10 times with maximum exercise).
Body Heat Control: In hot, humid weather, sweat doesn't work as well. The surrounding air is already warm and heavy with humidity, and it cannot absorb extra heat and sweat. So the body begins to warm up, and the heart begins pumping more blood to the skin to release the extra heat. Even if you sit still, your heart will beat faster. Have you ever felt tired after a day spent lounging on the beach? That fatigue comes from your heart working overtime to cool your body. If you sweat a great deal of water and lose enough minerals, you could develop one or more heat illnesses.
  • Danger(Heatstroke): The most dangerous heat illness is heatstroke. Heatstroke is a life-threatening medical emergency. The victim may develop headache, slurred speech, dizziness, faintness, hallucinations, seizures, and may even become comatose. Body temperature soars to 40 C (104 F) or more. The person becomes so dehydrated that the skin no longer sweats and is hot and dry to the touch.
  • Who's at Risk: Certain health conditions increase a person's risk of heat illness. Obesity, sweat gland diseases, diabetes, dehydration (a shortage of body fluids), malnutrition, low blood pressure, and heart disease all make it difficult for the body to regulate heat. In many instances, patients have more than one of these conditions. Older adults, especially, are more likely to have multiple health problems.
Variation of body temperature:
  • Exogenous Causes:
    • exposure to hot/cold air/water temperatures,hot/cold food or beverages,alcohol large-protein-rich meals, etc.
  • Endogenous Causes:
    • circadian variation,gender,ovulation,age and etc.
  • Physiological Variations In Normal Body Temperature
    • Digestion of food - rise 0. 5 to 1.0 F
    • Exercise (Vigorous) - rise to 102-104 F (return to normal within thirty minutes with rest or shower)
    • Diurnal Variation - low point early a.m.; peak in late afternoon, early evening. Variation varies - rarely up to three degrees, usually 1 to 2 F or may be reversed with changes in work habits.
    • Menstrual Cycle - rise of 0.5-0.75 F rectally at time of ovulation with drop back at menstruation. Absent with amenorrhea. (See page 23)
    • Pregnancy - continuation of above rise for about the first four months of pregnancy.
    • Warm Environment -slight increase (0.5 F)
    • Cold Environment - very slight drop in healthy adults; marked drop in infants and very old adults.
    • Emotion - slight temporary rise with emotion
Exercise and body temperature
  • The impact of activity on core body temperature is called masking. Studies have shown that masking varies as a function of circadian phase subjects performed a standard amount of exercise at regular intervals within the context of a forced desynchrony protocol to test whether the impact of this exercise on body temperature varies with circadian phase.
  • Methods: 22 healthy male subjects (age 20-25 yrs) were studied in a forced desynchrony protocol (sleep-wake cycle T = 20 hrs, 13.5 hours of wakefulness followed by 6.5 hours for sleep, continued for 6 subjective days = 120 hours. For 11 of them, a standard amount of exercise (70% VO2-max on a cycle trainer for 20 minutes + 5 minutes warming up and 5 minutes cooling down) was scheduled at 2 hour intervals during the 6 subjective days. This yielded short lasting peaks superimposed on the normal course of body temperature.
  • Results: Body temperature increased linearly during cycling up to an average of 0.7 OC. Subsequently, body temperature showed an exponential decline, being back to baseline before the subsequent exercise event occurred. For each individual and for each exercise session the increase in body temperature was measured by means of a regression of the data onto the individual’s average response.
  • Conclusion: Under the application of a standard amount of exercise a significant circadian modulation of masking is observed. Masking influences on human core body temperature are maximal near the circadian trough.
Temperature is taken every half an hour. In the graphs, the positions from 2 to 5 are where he is actually exercising

1.Pre-exercise temperature levels were similar in the afternoon (1330-1430: 37.06 ± 0.06°C) and at night (2230-2330: 37.13 ±0.09°C) but were significantly lower in the early morning (0400-0500:36.37 ± 0.07°C),

consistent with the well-known diurnal variationin resting core body temperature.

Exercise-induced elevationsof temperature were higher in the early morning (1.31 ± 0.08°C)than in the afternoon (0.96 ± 0.09°C, P < 0.05) or at night (0.89± 0.10°C, P < 0.05),

probably because the exercise-induced elevationwas superimposed on the normal early morning increase. The areasunder the curve for body temperature during exercise were similarat each time of day.

Circadian Rhythms:
  • CIRCADIAN RHYTHMS ARE BIOLOGICAL rhythms generated by an organism or group of organisms that have an intrinsic period of ~24hrs.
  • In humans,the site of the circadian pacemaker or biological clock is thesuprachiasmatic nucleus of the hypothalamus.
  • Circadian rhythms are physiological and behavioral rhythms and have a period of approximately 24-25hrs. This circadian clock is synchronized to the external cycles of light and darkness and social contact.
  • The synchronized rhythm is called the diurnal rhythm. Drowsiness increases as body core temperature falls, and also as this rises beyond the normal range.
  • In healthy individuals, the body temperature (oral temperature) is somewhere between 36.5 and 37.5. It slightly increases during the day since the morning (from 6:00 a.m.). The peak is reached at 6:00 to 10:00 p.m.
  • The lowest temperature is between 4:00 and 8:00 a.m. Diurnal variation depends on the activity throughout the day. Diurnal variations don't change in persons that work at night and sleep during the day.
  • Studies show that oral temperature revealed a maximum temperature in the early evening and a minimum in the early morning hours with a maximum-minimum range of 0.9 °C. It had been assumed for a long time that muscular activity (exercise) and digestive processes were the most important factors for generation of the CBT rhythm. CBT is determined both by changes in heat production and changes in heat loss, and concluded that heat production undergoes a circadian rhythm which is phase advanced by 1.2h with respect to the circadian rhythm of heat loss i.e. when heat production surpasses heat loss, CBT increases – transport of heat needs time.
Time Series: A time series is a sequence of observations which are ordered in time (or space).
  • If observations are made on some phenomenon throughout time, it is most sensible to display the data in the order in which they arose, particularly since successive observations will probably be dependent.
  • If you need to predict future values, Time Series can help. Collect new data and you can instantly update your predictions.
  • There are two main goals of time series analysis: (a) identifying the nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable). Both of these goals require that the pattern of observed time series data is identified and more or less formally described.
  • Here is an individual case where temperatures were taken over 160 days from a lady.
Smoothed out data: We wanted to extend our understanding of the Time Series data. We want to smooth out the data, if possible. We again used a moving average of 10. In this case, the graph looks like this: