Honors Contract Paper

8/14/2019 Honors Contract Paper

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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.).
http://diabetes.diabetesjournals.org/content/55/7/1995/F1.large.jpghttp://diabetes.diabetesjournals.org/content/55/7/1995/F1.large.jpg


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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.
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