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Jamie Yao
Professor Bruinsma
Physics 6A Honors
15 December 2009
Feedback between Physics and Physiology as a Means to Further the Field of Feedback
Feedback control of systems is a pervasive themeamong mechanical systems that
perform functions as different as controlling the speed of a steam engine and regulating the water
level of a trough. Despite the variability of devices and mechanisms that utilize feedback,
feedback itself may be essentially defined as using the measure of output as a means to regulate
said output (Benedek and Villars 442). The standards which determine the workings of
mechanical devices manifest themselves in important biological mechanisms such as protein
synthesis and viral function (Benedek and Villars 448). The feedback and stability theories that
lie at the core of how these mechanisms work are vital to understand from a clinical perspective;
for instance, feedback is the driving force behind requisites for life, including breathing and the
beating of the heart. Furthermore, physiological feedback failure lies at the root of disease such
as the uninhibited cell growth characteristic to cancer (Benedek and Villars 448). The principles
of mechanical physics lend us a useful perspective and approach with which to analyze and
understand feedback and control on a physiological level. Indeed,it was the invention and
development of mechanical devices that gave rise to the theory of automatic control (Benedek
and Villars 442). Conversely,biological examples may serve as cases useful for physicists in
constructing their own models of feedback and stability. The relationship between physics and
physiology with regards to feedback control may be casually referred to as feedback itself! This
paper will bridge physics and physiology by application of the physical principles operating
behind temperature and glucose feedback control to related research. Guided by George B.
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processes the control signal, by which the effector or actuator will produce an effect that will
lead to the output. However, disturbances, or an external load, will also additively influence the
actual output (Cruse). Once again, this output is measured by the sensor, which then feeds back
the information to the comparator. In contrast, an open loop system does not contain this
feedback loop (Boyd), as shown below:
Figure 2.Basic open loop system diagram.
In an open loop system, we must be familiar with an amount of input that will lead to a desired
output (Cruse). Typically, if a system is unpredictable, a closed loop system is more ideal
because it will be able to respond to changes in the load (Cruse). Within a closed loop system,
there are different types of controls that can be utilized depending on the nature of the changes in
the load. When the change in output is proportional to the difference between the reference input
and the output, the system is said to be under proportional control. Other forms include the
derivative control and integral control, where the input is proportional to the derivative or
integral, respectively, of the output with respect to time (Benedek and Villars 462). Typically,
derivative control functions as a response to a quick change in the output, whereas integral
control operates for long-term deviation from the reference input (Hugh).
THERMOREGULATION OF THE HUMAN BODY
The process of thermoregulation is under feedback control, as shown in the diagram below.
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Figure 3.Feedback control of thermoregulation (Weller).
Though presented in a different format than the general feedback loop of Figure 1, we can see
that thermoregulation does indeed operate under feedback control. A comparison between a set
point and thermal signals, or the output, leads to an error signal that drives effector signals.
These effector signals then produce effects such as sweating or vasodilation as a response to the
load error signal.
While a biological portrayal is helpful in understanding thermoregulation, it is also useful
to derive an equation describing the temperature change of the body, which we can use as a tool
for subsequent thermoregulation analysis. We derive the equation with guidance from Benedek
and Villars. The bodys net heat rate (dQ/dt)totalis a summation of different components for heat
production and loss. For heat production, the term (dQ/dt)metaccounts for metabolic and physical
activity. For heat loss, we use (dQ/dt)out to describe the passive forms of heat loss: convection
and radiation. In addition, (dQ/dt) control describes the rate for the heat flow that stems from the
feedback control system. The usage of the term heat flow, as opposed to gain or loss, is
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purposeful; heat movement related to the control system may be in the form of either production
or loss of heat, depending on the system temperatures deviation from the set point. Therefore,
dQdttot=dQdtmet+ dQdtcontrol- dQdtout
The minus sign for (dQ/dt)out indicates that it is a loss of heat; the term (dQ/dt)control may or may
not also be a negative value. On the left side of the equation, we can define the total heating rate
as follows:
dQdttot=CdTbodydt
where Cis the human bodys heat capacity. For the right side of the equation, it is conceptually
helpful to treat each of these terms one by one. The metabolic rate is:
dQdtmet=m Po
wherePois defined as the basal rate whereas mis a factor from one to 20 that describes the
metabolic rate. For example, m = 1 would be equivalent to the basal rate, whereas a factor ofm =
20 would mean a metabolic rate 20 times the basal rate due to physical activity. The term for
heat loss due to passive heat loss considers both convection and radiation:
dQdtout=dQdtconvection+dQdtradiation
= 1Tskin- Ta+ 2Tskin- Ta
= Tskin- Ta
Here, Ta is the ambient temperature, and is a value dependent on clothing worn, wind speed,
and body surface area (BSA), with higher values for less clothing, higher wind speeds, and larger
BSA. In this analysis we will focus the control term only in terms of the sweating mechanism, as
it relates to the experiment that we will highlight. Because sweating results in cooling of the
body, the sign of the control term here will be opposite to that of metabolic rate and in the same
direction as convection and radiation.
The equation for sweating is based upon empirical evidence that sweating begins once
the bodys core temperature is higher than a threshold of 36.85 C (Benedek and Villars 511).
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Once the core temperature hits this point, the sweating rate is proportional to (Tcore 36.85 C):
-dQdtcontrol=KTcore-36.85 f
withKhaving the value 750 kcal/(h C) here. Therefore our final overall equation for the net
heating rate of the body is:
CdTbodydt=m Po- Tskin- Ta+ K(Tcore-36.85 )
This overall equation shows us that there are several factors that affect rate of temperature
change. It is useful to explore and manipulate this equation as a way of understanding the
variables that affect the heating rate of the body. Indeed, the design of the experiment we will
discuss was formulated based on the principles illustrated by the above equation as well as
observations found by prior research on fitness level and sweating.
EXPERIMENT EXPLORATION: PHYSICAL TRAINING AND SWEATING
Previous studies had shown that people with short-term exercise training have increased
thermal regulation, as indicated by an elevated level of sweating (Yamamuchi et al.). However,
the literature also states that people with long-term exercise training have decreased levels of
sweating during exercise (Yamamuchi et al.). This apparent discrepancy suggests that the long-
term adaptation to extensive exercise differs from that of the short term. In order to better study
the long-term adaptation, Yamamuchi et al. performed an experiment to compare non-athletes
and athletes (defined as having long-term physical training) during moderate bicycle activity of
80 Watts for 30 minutes. Factors measured at different time points included the sweating rate
Msw, the frequency of sweat expulsionsFsw, and skin and tympanic temperature (temperature of
the ear canal tympanic membrane) Ts and Tty, respectively.
Considering the variables that affect the rate of temperature change is important when
comparing the two groups of non-athletes versus athletes. Doing so ensures that the groups are
controlled for all other variables except the one being tested, that is, the absence or presence of
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long-term exercise training. Data were collected on the subjects in both groups to compare for
any significant differences that could possibly lead to biased results:
Figure 4. Table of mean measured characteristics of the athletic and non-athletic groups.
(Yamamuchi et al.)
The equation that we derived above (copied below) gives us insight into what variables may
influence our results:
CdTbodydt=m Po- Tskin- Ta+ K(Tcore-36.85 )
Age and height are not explicit variables in the equation but may influence metabolic rate and
have other unknown effects. BSA is a factor in determining the value of , so its consistency
between the groups is important (Benedek and Villars 507). Focusing on the left side of the
equation, we can break down heat capacity Cinto specific heat capacity Cs mass of the
subject. Therefore, the larger the mass of the subject, the larger the heat capacity will be
consequently. When dividing through by the heat capacity to obtain the value of rate of
temperature change, a larger heat capacity in the denominator will give us a smaller rate of
change of temperature. From the data collected, the researchers concluded that there was no
significant difference in masses between the groups. Such a check is necessary before proceeding
with the experiment in order to avoid possible bias.
By the same strand, we take constants and Tato be the same across both groups as a
result of the controlled environments of the experimental setup (and because BSA values are
similar). Additionally, the values ofTskinand Tcore (which we take to be equivalent to Tty) were
reported not to be statistically different between the two groups experiment initiation. Though we
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might expect a higher basal metabolic rate in the athletes, overall metabolic rates were not
significantly different based upon measurements obtained of the oxygen consumption prior to
and at the end of the experimental exercise. Maximal oxygen consumption, as expected, differed
significantly between athletes and non-athletes, because higher fitness level correlates to a higher
maximum oxygen capacity (Benedek and Villars 403).
The researchers determined the body temperature Tbody as a weighted average derived
from the tympanic temperature of the tympanic membrane of the ear canal in addition to the skin
temperature Tskin from the chest, forearm, and leg:
Tskin=0.5 Tchest+ 0.14 Tforearm+ 0.36 Tleg
The ratio of 0.9 to 0.1 to determine body temperature is commonly used in studies in hot
environments (Sawka, Castellani):
Tbody=0.9 Ttympanic+ 0.1 Tskin
Now let us see if the results correlate with basic physics. The equation for the rate of sweating is:
-dQdtsweating=KTcore-36.85 f
SinceKis constant between the two groups, we need only look at Tcoreto determine any
difference between the athletic and non-athletic groups in terms of the sweating rate. The figure
below shows us the data collected for the tympanic temperature, which we liken to the core
temperature.
Figure 5. Tympanic (core) temperatures (C) of non-athletic and athletic groups. (Yamamuchi et
al.)
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A view of the graph suggests no significant difference between the two groups in terms of core
temperature, as both the values and the trends correlate well. This was confirmed by quantitative
analysis. Since Tcore, athletic Tcore, non-athletic, according to our calculations, dQdtathletic should
also be approximately equal to dQdtnonathletic. Indeed, the researchers found no significant
differences between the local sweat rates of the athlete and non-athlete groups.
EXPERIMENT EXPLORATION: EFFECT OF LOWER CORE BODY TEMPERATURE
IN TRANSGENIC MICE
Another experiment studying thermoregulation of the body is one that achieved the
lowering of the core body temperature in transgenic mice. The rationale behind Conti et al.s
method was that a hypothalamus, acting as the bodys thermostat, that sensed a higher
temperature would activate certain effector responses to lower the temperature. This justification
is founded upon the general closed loop mechanism. To successfully lower the core temperature,
the researchers depended on the negative feedback system to lower the temperature if the sensors
felt a higher temperature. To do this the authors looked towards the uncoupling protein 2
(UCP2), which generates heat via the proton gradient in oxidative phosphylation. By
overexpressing UCP2 in hypocretin neurons, the researchers were able to raise the temperature
proximal to the hypothalamus. As a result, Tcore lowering in these transgenic mice was validated
by comparisons between the wild-type and transgenic mice.
Conti et al. found that transgenic mice lived longer than the wild-type mice, with a
median life span 12% and 20% greater in transgenic male and female mice, respectively:
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Figure 6.Proportion of mice in sample pool surviving at given age.
Though the reason for this phenomenon is unknown, the authors suggest that it may be a result of
lessened metabolic burden as a function of a lower core temperature. This proposition stems
from the observation that transgenic mice lost a significantly greater amount of weight than the
wild-type mice did following an imposed food deprivation:
Figure 7. Quantification of weight loss (normalized for estimated metabolic burden) in wild-typeand transgenic mice by sex following food deprivation.
Lesser weight loss indicates that the transgenic mice expended less energy. Conti et al. propose
that this indicates a more efficient metabolism that is a result of a lower energy requisite needed
to maintain a lower core body temperature. Let us see if this statement stands up to physics
standards. By integrating our general equation for the net heating rate of a body, we have:
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CdTbodydt=dQdtmet+ dQdtcontrol- dQdtout
which simplifies to:
CTbody= Qmet+ Qcontrol- Qout
This equation supports the idea that decreased temperature correlates with decreased metabolic
activity! We can approximate the body temperature here as the core temperature. From this
equation we can see that Tbody and Qmetare directly proportional to each other. Therefore, when
the body temperature, or core temperature, decreases, the heat produced by metabolic activity
also decreases. Thus the researchers explanation for the transgenic mices less severe weight
loss as a function of a lower metabolic demand is feasible.
GLUCOSE CONTROL: A GENERAL APPROACH
Glucose control is another physiological example of feedback and control. The glucose
control system functions via the below equation (Benedek and Villars 514):
dQdtcontrol system=K(Cs- C)+ KDd(Cs- C)dt + Rave*f
where Q is the total mass of blood glucose, Cis the glucose concentration with dimensions
[M/V], and Cs is the set point for glucose concentration. This equation illustrates that glucose
control is under three types of controls: proportional, derivative, and integral. The first term,
representing proportional control, contains the constant of proportionalityKwith dimensions
[V/T] and describes the initial response to deviation from the basal glucose level (Benedek and
Villars 515). This initial response consists of either the release of insulin when C> Cs or
glycogenolysis when C
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Insulins function in glucose control is to lower blood glucose levels by aiding in the
uptake of glucose from the blood into muscle and fat cells. Further, it initiates the insulin
signaling pathway in liver cells which ultimately converts glucose to glycogen, further
contributing to the effect of lowered blood glucose levels. When the body is unable to regulate
glucose levels due to lack of insulin such as in diabetes mellitus Type I, we can solve this
problem by supplementing exogenous insulin. A device that can sense insulin levels and deliver
insulin accordingly operates in a closed-loop mechanism and is termed an artificial pancreas.
One such device utilizes an algorithm containing proportional, derivative, and integral
*Some variables in the equation presented in the original paper have been changed to maintain consistency throughout this paper.
components much like the glucose control system itself (Panteleon et al.):
PIDt= KC-Cs+KTD dGdt+ KTIC- Cs dt*
The proportional term contains a valueKin units h-1 per mg/dL and indicates the insulin delivery
rate due to glucose level deviation above the set point (note that here insulin delivery is only
needed when glucose levels are higher than the basal level Cs). The derivative term integral term
in this equation describes the insulin delivery response that occurs when (dC/dt) is positive.
Finally, the integral element, much like in the glucose control system, functions for enduring
hyperglycemia. In the equation, Cs, TD, and TI were constants determined by computer modeling.
The gainKis proportional to the total daily dose TDD of insulin, a value obtained from open
loop trials that found out a value ofTDD that would lead to a particular glucose level output. In
this experiment, different gains were tested in order to compare their effects. The gain value, also
called the open loop gain, is useful for comparison of closed loop and open loop systems.
Typically much greater than one, this value is an indication of the efficacy of the feedback
response to variation in the load (Benedek, Villars 464). It is a factor measuring the difference of
change in output as a result of the change in load between open loop and closed loop systems.
For example, if applied for glucose levels, a gain of 20 says that the changes in the glucose level
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as a result of eating are reduced by 20 in the controlled system as compared to the uncontrolled
system. In this experiment, the gains were based upon TDD: 0.5 TDD, TDD, and 1.5 TDD,
in increasing gain order. In other words, 1.5 TDD gives the greatest insulin dose and thus
represents a greater gain, or lesser change in glucose level, as a function of increased external
load.
Experimental results obtained from testing the insulin delivery system on diabetic canines
agree with intuitive physical concepts:
Figure 8. Glucose and plasma insulin levels for three different gains tested versus time
(Panteleon et al.).
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With increasing gain, greater amounts of insulin are administered. Subsequently, glucose levels
are lower and therefore closer to the basal glucose concentration for increasing gain. Before the
meal is administered at t = 240 minutes, both glucose and insulin levels are relatively constant
among the different gains. Though peak insulin levels were similar among the different gains,
peak glucose levels were significantly different, with higher lower maximum glucose levels for
increasing gain.While the goal is to lower glucose levels so that they are close to the basal level,
it is possible to overshoot the target level, resulting in hypoglycemia. As may be expected, this
occurred with greater frequency for greater gain: once for 0.5 TDD, three times for TDD, and
two times for 1.5 TDD. Thus, while it may seem that 1.5 TDD is more ideal than the other
gain options based on the data shown, we must consider the possible overshooting effect in mind
(Panteleon et al.).
The feedback control system is a basic concept that manifests itself in complex systems.
Whether biological or mechanical, the feedback system is characterized by representative
qualities so that the closed loop system may be simply defined. Physiological examples such as
temperature and glucose level stability are crucial to human being survival. Study of the
feedback mechanisms involved has led to medicine advances that can counteract any failure or
deviation of the feedback system from its norm. When fever results from resetting of the set
point, we can use anti-pyretic drugs to lower the body temperature. When Type I diabetes
patients are unable to produce their own insulin, we can supplement endogenous insulin via
insulin delivery systems that function according to the feedback mechanism of glucose. Research
on feedback systems, whether via bench, clinical, or modeling methods, helps us to make further
advances for the future. However, fundamental physics which has endured for years upon years,
can provide a means of experimental design or serve as a post-experimentation analysis tool.
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Works Cited
Benedek, George B., and Felix M.H. Villars.Physics with Illustrative Examples from Medicine
and Biology: Mechanics. New York: Springer-Verlag, 2000. Print.
Boyd, S. Lecture 12: Feedback Control Systems: Static Analysis.Electrical Engineering 102.
Stanford U., n.d. PDF file. . 29
November 2009.
Conti B, Sanchez-Alavez M,Winsky-Sommerer R, Morale MC, Lucero J, Brownell S, Fabre V,
Huitron-Resendiz S, Henriksen S, Zorrilla EP, de Lecea L, Bartfai T. Transgenic mice
with a reduced core body temperature have an increased life span. Science 314(5800)
(2006):825-8. . 12
November 2009.
Cruse, Holk. Neural Networks as Cybernetic Systems. Department of Biological Cybernetics
and Theoretical Biology, Bielefeld University. Brains Minds Media. . 20 November 2009.
Hugh, Jack. Feedback Control Systems. 2003. Section 8.3. PDF file.
. 20 November 2009.
http://www.ncbi.nlm.nih.gov/pubmed?term=%22Conti%20B%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Sanchez-Alavez%20M%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Winsky-Sommerer%20R%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Morale%20MC%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Lucero%20J%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Brownell%20S%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Fabre%20V%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Huitron-Resendiz%20S%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Henriksen%20S%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Zorrilla%20EP%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22de%20Lecea%20L%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Bartfai%20T%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://stke.sciencemag.org/cgi/content/full/sci;314/5800/825http://www.ncbi.nlm.nih.gov/pubmed?term=%22Sanchez-Alavez%20M%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Winsky-Sommerer%20R%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Morale%20MC%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Lucero%20J%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Brownell%20S%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Fabre%20V%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Huitron-Resendiz%20S%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Henriksen%20S%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Zorrilla%20EP%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22de%20Lecea%20L%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://www.ncbi.nlm.nih.gov/pubmed?term=%22Bartfai%20T%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstracthttp://stke.sciencemag.org/cgi/content/full/sci;314/5800/825http://www.ncbi.nlm.nih.gov/pubmed?term=%22Conti%20B%22[Author]&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstract8/14/2019 Honors Contract Paper
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Panteleon AE, Loutseiko M, Steil GM, Rebrin K. Evaluation of the effect of gain on the meal
response of an automated closed-loop insulin delivery system.Diabetes 55
(2006):19952000. . 10
December 2009.
Sawka, M.N., Castellani, J.W. How hot is the human body?Journal of Applied Physiology 103
(2007): 419-420. .
Weller, A.S. Body temperature and its regulation.Anesthesia and Intensive Care Medicine. 6
(2005): 206209. . 11
December 2009.
Yamauchi M., Matsumoto T., Ohwatari N., Kosaka M. Sweating economy by graded control in
well-trained athletes.European Journal of Applied Physiology 433 (1997):675678.
. 13 November 2009.
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