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A Statistical Analysis of Human Body
Temperature

By Dhanalakshmi Pantangi Praneetha
Mukhatira Yaping Sun
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• Introduction
• 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.

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• 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 (0K) 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.

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• 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 0K (-273.15 Celsius).
  
• Devices
• The Liquid-in-glass Thermometer
• Digital thermometers
• Electronic thermometers
• Infrared Ear Thermometers
• Dot matrix or phase change thermometers

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• 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

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• STUDY CONDUCTED BY
• 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.
• MEASUREMENTS--
• 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.

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• Temperature Regulation of the Human Body

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 36.8C and increases rapidly as
the skin temperature rises above this value.

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• 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

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• 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.

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• 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).

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• 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).

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• 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.

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• Variation of body temperature
• Exogenous Causes
• exposure to hot/cold air/water temperatures,hot/co
  ld 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

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• 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
  individuals 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.

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• Temperature is taken every half an hour. In the
  graphs, the positions from 2 to 5 are where he is
  actually exercising

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1.Pre-exercise temperature levels were similar in
the afternoon (1330-1430 37.06  0.06C) and at
night (2230-2330 37.13  0.09C) but were
significantly lower in the early morning
(0400-0500 36.37  0.07C), consistent with the
well-known diurnal variation in resting core body
temperature. Exercise-induced elevations of
temperature were higher in the early morning
(1.31  0.08C) than in the afternoon
(0.96  0.09C, P lt 0.05) or at night (0.89
 0.10C, P lt 0.05), probably because the
exercise-induced elevation was superimposed on
the normal early morning increase. The areas
under the curve for body temperature during
exercise were similar at each time of day.
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• Circadian Rhythms
• CIRCADIAN RHYTHMS ARE BIOLOGICAL rhythms
  generated by an organism or group of organisms
  that have an intrinsic period of 24 hrs.
• In humans, the site of the circadian pacemaker
  or biological clock is the suprachiasmatic
  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 600 a.m.). The peak is reached
  at 600 to 1000 p.m.
• The lowest temperature is between 400 and 800
  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.

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• 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.

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• 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