CD
0A NON-DIMENSIONAL ANALYSIS OF
CARDIOVASCULAR RESPONSE TO COLD STRESS
PART II: DEVELOPMENT OF THE NON-DIMENSIONAL PARAM ETERS
D T IC J" Sharon A. Starowicz, M.S.SELECTE Biomedical Engineer
MAR2 M U.S. Food and Drug Administration
D 7, Silver Spring, Maryland 20910
TD
Daniel J. Schneck, Ph.D.
Professor of Engineering Science and Mechanics
Head, Biomedical Engineering Prograr
Virginia Polytechnic Institute and State University
227 Norris Hall
Blacksburg, Virginia 24061
DTSTR1MU'r1ON STATEMENT A-Approved fot public releaze(
89 3 24 022
SECURIrY CLASSiFICATION OF rHiS PAGE
REPORT DOCUMENTATION PAGE ' /
Ia. REPORT SECURITY CLASSIFICATION lb. RESTRICTIVE MARKINGS
w Unclassified2.. SECURITY CLASSIFICATION AUTHORITY 3 DISTRIBUTION /AVAILABILITY OF REPORT
Approved for public release;2b. DECLASSIFICATION/DOWNGRADING SCHEDULE distribution is unlimited
4. PERFORMING ORGANIZATION REPORT NUMBER(S) S. MONITORING ORGANIZATION REPORT NUMBER(S)
NMRI 86-80
6a, NAME OF PERFORMING ORGANIZATION i6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATIONNaval Medical Research (If applicable) Naval Medical Command
6c. ADDRESS (Cty, State, and ZIP Code) 7b. ADDRESS (City, State, and ZIP Code)
Bethesda, Maryland 20814-5055 Department of the NavyWashington, D.C. 20372-5120
8a. NAME OF FUNDING/SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION Naval Medical O (f applicable)
Research and Development Command I ,
Sc. ADDRESS (City, State, and ZIP Code) 10. SOURCE OF FUNDING NUMBERSBethesda, Maryland 20814-5055 PROGRAM PROJECT ITASK 'WORK UNIT
61153N MRO41.01 06A
11. TITLE (Include Security Classification)
A NON-DIMENSIONAL-ANALYSIS OF CARDIOVASCULAR RESPONSE TO COLD STRESS
PART II: DEVELOPMENT OF THE NON-DIMENSIONAL PARAMETERS [PART I: NMRI 83-51]
12. PERSONAL AUT'OR(S)Starowicz SA, Schneck DJ
13a. TYPE OF REPORT 1 3b. TIME COVERED i14. DATE _F lP PqP T Year, Month, Day) uS. PAGE COUNTTechnical Report IFROM TO 115
16. SUPPLEMENTARY NOTATION
17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)
FIELD GROUP SUB-GROUP Hypothermia Dimensionless Parameters
_ _ __ Tempe.ature __. Cardiovascular ControlVascular System Blood
19. ABSTRACT (Continue on reverse if necessary and identify by block number)
20. DISTRIBUTION /AVAILABILITY OF ABSTRACT ' 21. ABSTRACT SECURITY CLASSIFICATION
(MUNCLASSIFIEDIUNLIMITED 0 SAME AS RPT. 0 DTIC USERS Unclassified
22a. NAME OF RESPONSIBLE INDIVIDUAL . 122b TELEPHONE (include Area Code) 22c. OfFICE SYMBOL
Phyllis Blum, Information Services Division 202-295-2188 1ISD/ADMIN/N kI
DD FORM 1473, 84 MAR 83 APR edition may be used until exhausted. SECURITY CLASSIFICATION OF THIS PAGE
All other editions are obsolete. UNCLASSIFIED
.... : -:,.. o . ¢'..; - ... -• .' '.____-- __" __'-, ___, ______. ______--- __- ___" ___. _________.. _ .. . ...
TABLE OF CONTENTS
Page
Chapter
I Introduction and Statement of the Problem .................... 1
II Historical Background ...................................... 6
III Method of Analysis ......................................... 9
A. The Buckingham Pi Theorem .............................. 9
B. Simplification and Physical Significance ofDimensionless Parameters .............................. 13
IV Tabulated Results of the Analysis .......................... 14
V Discussion of Results ...................................... 18
V!I Conclusion................................................ 25
References......................................................... 29
Appendix.......................................................... 31
Table 1 - Tabulation of Derived Dimensionless Parameters ... 32
A. Blood................................................ 32
B. Heart................................................ 43
C. Vascular System ....................................... 58
D. Miscellaneous........................................ 80
Table 2 - Derived Fundamental Scales Associated with Electro-
thermodynamic Effects ..................................... 86
Table 3 - Other Derived Scales Associated with Electrotherno-
dynamic Effects.......................................... 87
Table 4 - List of Symbols Used in Table 5..................... 88
TABLE OF CONTENTS (continued)
Page
Table 5 - Derived Dimensionless Parameters Written in Termsof Traditional Non-Dimensional Numbers Related to Fluidand Thermodynamic Theory ................................ 91
Table 6 - List of Variables Which Are Already Dimensionlessby Definition .............................................. 99
Table 7 - Other Variables That Can Be Associated with Cardio-vascular Function and Thermoregulation .................. 103
Table 8 - Enzymes ............................................... 107
Table 9 - Hormones .............................................. 09
Table 10 - Nutrients ............................................
Table 11 - Vitamins ............................................. 113
Table 12 - Buffering Ions, Minerals and Electrolytes, TraceElements, Blood Gases, Byproducts of Metabolism ......... 114
Accesion
For
NTIS CRA&JOTIC TAi8 0Unannounced 0
By
AvjJ!.Jjt-ty Codes
D Avdi ,odlor
Dist
UL ca
i v f -.,
CHAPTER I
Introduction and Statement of the Problem
The thermoregulatory function of the cardiovascular system is ex-
tremely complex. It involves numerous physical and chemical parameters
that interact )o maintain a relatively constant temperature within the
body core, an anatomical region containing organs vital to the sustenance
of life.4Jnder conditions of cold, the body utilizes a variety of feed-
back control regulatory mechanisms that attempt both to decrease heat loss
to the environment and increase heat production. The primary effector of
such control is the cardiovascular system, which has the ability to rapid-
ly change blood flow patterns throughout the body in response to this need.
The reaction of the system to a moderately cold stimulus has been
studied fairly extensively and is understood quite well -t 3 Not so
well understood, however, is what happens when one is subjected to ex-
tremes of cold, where body reactions can often be quite adverse. Not
only is performance greatly restricted in the cold environment due to
impaired musculoskeletal function, but a host of pathologic conditions
result from the inability of the system to function under extremely low
temperatures. In fact, the same mechanisms that attempt to protect and
maintain the body in the presence of moderately cool temperatures, may
indeed promote the destruction of the system when it is subjected to
extremes in cold.
Relatively little is known about the physiology of temperature
1|
2
regulation during prolonged periods of cold exposure. The complexities
of the cardiovascular system even under normal operating conditions are
vast. The fluid, blood, possesses certain non-Newtonian, anisotropic,
and viscoelastic properties that directly influence its ability to trans-
port heat. In addition to carrying heat, blood is responsible for trans-
porting various biochemical constituents that are directly involved in
thermoregulatory processes. The properties of blood are also highly
temperature-dependent. For example, as the fluid is cooled it becomes
more viscous and harder to pump, creating a tendency toward decreased
blood flow.
An equally important constituent of cardiovascular thermoregulatory
response is the vascular system, which provides the "pipes" through which
the fluid is pumped. Both heat and mass transport occur across the blood
vessel walls and the ease with which blood can be pumped through them is
directly dependent upon various temperature-related elastic properties of
the vessels themselves. In addition, the blood vessels are able to regu-
late the pathways of blood flow through local vasoconstrictive mechanisms
in response to a cold stress.
The heart serves as the pump for the system and provides the energy
needed to drive the blood. Under continuous nervous control, it can adjust
its pumping rate to change cardiac output as needed.
In addition to these "hardware" components, one must also consider
the intrinsic control mechanisms that govern the overall system response
to any external stimulus. This would include the endocrine system as well
as the central and autonomic nervous systems.
3
Any approach to studying the effects of cold on the cardiovascular
system must necessarily account for all the governing factors mentioned
above. This is to ensure model accuracy, since so many aspects of the
system are interrelated and dependent on one another. The analysis must
seek to isolate as many thermal, mechanical, and chemical properties of
the system as possible, toward the ultimate goal of obtaining a detailed
understanding of how these properties interact to protect body function
S 14 effectively from temperature extremes in assaulting environments. With
Ahis) in mind, the Aorkiwhich follows -escribes a non-dimensional approach
which was taken to describe cardiovascular function
Over six hundred physical and chemical Variables that govern the
thermoregulatory function of the cardiovascular system have been identi-
fied [13], and even this impressive list is far from exhaustive. In this
study, the variables related to properties of blood, the vascular wall,
the heart, and the cardiovascular control system were defined using
dimensions of mass, length, time, temperature, and charge. From these,
a working set of dimensionless parameters was developed using the Buck-
ingham Pi Theorem.(see Chapter III and Table I of Chapter IV). -This
allowed the thermal, mechanical, and chemical properties of the cardio-
vascular system to be coupled through the non-dimensionalization process.
In order to obtain insight into the physics of the problem and to under-
stand what the dimensionless groupings represent, these parameters were
simplified and related to one another through geometric ratios and non-
dimensional numbers common to the fields of fluid mechanics, solid and
fluid heat conduction and convection, viscoelasticity, and electrochemical
4
diffusion (see Tables 4 and 5). On this basis, comparison of the param-
eters in terms of their relative significance to the problem was made.
In addition, various scales were derived that are associated with elec-
trothermodynamic processes and these were used to identify the physical
significance of each parameter (see Tables 2 and 3).
Such a preliminary non-dimensional approach exploits a powerful
technique for recognizing the fundamental aspects of the problem before a
more complicated mathematical formulation is attempted. Because one can
not initially know all the details associated with the response of the
cardiovascular system to cold stress, and because there exist numerous
experimental limitations that inhibit comprehensive study, a non-dimen-
sional analysis provides a first order understanding of physical processes
associated with the problem. This presents a foundation for future
mathematical treatment.
In addition to identifying what experimental parameters might be
useful for modeling studies, this analysis has direct application to the
military, where prediction of physiologic response to adverse combat
situations is often desired. Along these lines, relevant and measurable
design parameters for protective clothing and gear may be proposed to
enhance natural thermoregulation and compensate for adverse environmental
reaction. Going one step further, the development of design parameters
that may be useful in optimizing protective gear, and the suggestion of
training methods to affect conditioning or adaptation to a cold environ-
ment, may all result from studies of this kind. By quantifying the
final parameters and exploring their variability among individuals, a
basis for clinical diagnosis and treatment may be established, as well
as a protocol for predicting one's susceptibility to cardiovascular
stress in a cold environment.
CHAPTER II
Historical Background
The use of dimensional analysis is not recent. The development
of the Buckingham Pi Theorem in 1914 provided a systematic mathematical
approach to determine dimensionless groupings that contained variables
pertinent to a given problem [6]. This technique is exploited in
the following study and is explained in detail in Chapter III.
In 1927, Lambert and Teissier [10] first dealt with the question
of circulatory similitude by proposing that the cardiac cycle and other
biological periods are proportioiial to the length dimension of the body.
Historically, similarity studies of the cardiovascular system have been
based on well-established hydrodynamic principles [10]. However, such
principles have often been used only to define local hemodynamic similar-
ities without regard to the system as a whole. Current trends in this
area combine such traditional methods with modern pulse transmission
theory and cardiac dynamics, in an attempt to establish similarity criter-
ia for the entire system that directly relate the physiological response
of the system to its structural design [10].
A variety of cardiovascular phenomena have been explored using
similarity criteria and dimensional analysis. McComis, Charm, and Kurland
[11] attempted to characterize pulsating blood flow by using dimensional
analysis as a method for obtaining equations which describe various
pressure-velocity relationships. By investigating the parameters that
6
7
mignt influence the pulsating flow of blood through small tubes, and
organizing these through dimensional analysis, they were successful in
characterizing the steady flow of blood through small glass tubes.
Further experimentation allowed the relationship between such parameters
to be expressed in a simple form.
Another area where dimensional analysis has found great applicability
is that of determining optimal design features of the cardiovascular
system. For example, the recent works of Li and Milnor [10] have
suggested that the arterial pulse transmission path length and wavelength
are of such a ratio that the amount of external work performed by the
ventricle at the resting heart rate is at a minimum. Using allometric
equations for the given variables, a relationship may thus be derived for
either ratio, and such may then be used to define a design feature of the
system. Similarly, other dimensionless parameters may be used to charac-
terize cardiac function and from these, the basis for optimal design of
cardiovascular devices may be derived.
In addition to the utilization of non-dimensional analysis as it
relates to design and experimentation, it has served as a means for making
highly sophisticated mathematical analysis more manageable and applicable.
In a study involving flows in the entrance regions of circular elastic
tubes, Kuchar and Ostrach [8] made use of a non-dimensionalization scheme
in order to obtain an approximate solution satisfying a simplified set of
partial differential equations. Given the complexity of the equ3tions
for fluid velocity distributions, pressure distributions, and motions of
the tube wall, an exact solution becomes impossible to obtain. By
8
introducing the non-dimensionalizing transformations for the variables
involved into the Navier-Stokes equations and simplifying, significant
non-dimensional fluid parameters are obtained as coefficients. These
parameters contain the essential physics of the problem under investiga-
tion and, depending on their relative magnitudes, may be neglected if
shown to be insignificant to the overall problem. In so doing, a simpli-
fied and more manageable set of partial differential equations is obtained
which still contains the basic physics of the problem. The same technique
is applied to the equations governing the motion of the tube wall. A
similar non-dimensionalization scheme was used in the work of Schneck
[16] to examine the phenomenon of pulsatile flow in a diverging circular
channel.
Although the power of the technique ;s unquestionable, it has not
been exploited to its fullest extent to describe the overall function of
the cardiovascular system, particularly with regard to its thermoregula-
tory response. By reviewing the literature of past and present it becomes
evident that the non-dimensional scheme is used as a tool in the simpli-
fication of equations governing specific cardiovascular phenomena only.
It does not appear to be used as a method of modeling the way in which
each aspect of the system interacts with one another and to what extent.
It is this author's desire to explain more fully the integrated function
of the cardiovascular system from the standpoint of heat and mass
transport, and to do so by developing a set of dimensionless parameters
that reveal the essential physics of the system without regard to complex
mathematical analysis or sophisticated experimentation.
CHAPTER III
Method of Analysis
A. The Buckingham Pi Theorem
"A non-dimensional parameter or variable is any quantity, physical
constant, or group of these formed in such a way that all of the units
identically cancel" [16].
Such a statement is the basis for the Buckingham Pi Theorem. Devel-
oped in 1914, it provides a systematic method to develop a finite number
of dimensionless parameters from a'group of variables, where a fixed
number of these variables are repeated in each parameter. In order to
initiate such a scheme, it must first be determined which dimensions are
to be considered fundamental. Most commonly, the choice for these are
mass, length, and time. However, because the problem at hand is complex
and involves variables representing thermal and electrical properties as
well, temperature and charge must be added for a total of five fundamental
dimensions. They are represented by the symbols M, L, T, e, and q,
respectively.
Once this is determined, each variable must be written in terms of
the fundamental dimensions, raised to some appropriate exponential power.
For example, mean arLerial blood velocity would be written as L1T - I ,
while fluid shearing stress would be represented by M1L-1T- 2 . Each of
the total of k (about 600) variables defined in Reference [13] and summa-
9
10
rized in Chapter IV (Table 1) were dimensioned in such a fashion.
The next step in the non-dimensionalization scheme is to select
n variables from among the total. These n variables will form the basis
of the technique in the sense that they will be inherent in all the
final dimensionless parameters. In this case, k is approximately equal
to six hundred and n = 5 (representing the number of fundamental dimen-
sions chosen). The choice for the five starting variables is essentially
arbitrary except that they must contain among them all five fundamental
dimensions. Since this study specifically addressed heat transport pro-
cesses, this author chose variables which reflect thermal concepts related
to the heat transport characteristics of blood. The variables chosen
were: Thermal Conductivity of the Blood (kt): MlLIT-36 -1 , Total Thermal
Capacity of the Blood (C): MIL 2T-2e-1, Specific Heat of the Blood
at Constant Pressure (cp): L2 T 26-1, Convection Coefficient of the
Blood (film coefficient, h): MT-36 "1, and the Faraday Constant (F):
M-1 q1 . These variables are used as "repeating variables" that can be
grouped with any of the remaining variables to determine each new dimop-
sionless parameter.
The essence of the Buckingham Pi Theorem states that, for the above-
chosen variables, an equation may be written which has the form:
kt aCbcp chdFe( )1 = MOLOT0e0qO
The blank indicates where each of the remaining variables is to be inserted.
Rewriting each variable in terms of its own hasic dimensions, the
]1
equation becomes:
(MILlT- 3 8-1 )a . (MIL2T- 20-l)b . (MOL 2T-2-1)c . (MILOT- 3 -l)d
(M-lLOTOOOql)e (_)1 = MOLOTOOOqO
By replacing the blank with each of the remaining k - n variables
individually and by equating corresponding coefficients, five equations
will be obtained that can be solved simultaneously for each of the five
lettered exponents.
For example, in order to create the dimensionless parameter involving
the electrical resistance of the vascular wall, R*, having the dimensions
MIL 2T-160q-2 , one would insert this quantity into the above equation
and solve accordingly:
M: (1 a) + (1. h) + (0 c) + (1 d) + (-1 e) + (1) 0
L: (I * a) + (2 * b) + (2 • c) + (0 d) + (0 e) + (2) = 0
T: (-3 • a) + (-2 * b) + (-2 • c) + (-3 • d) + (0 • e) + (-1) = 0
e: (-1 a) + (-I b) + (-I c) + (-I d) + (0 e) + (0) 0
q: (0 a) + (0 b) + (0 . c) + (0 . d) + (i - e) + (-2) 0
or
a + b +d -e+ = 0
a + 2b + 2c + 2 0
-3a - 2b - 2c - 3d - I = 0
-a -b c - d + 0 = 0
e- 2 =0
12
Solving these simultaneously for the exponents:
a =-4
b= 2
c = -1
d= 3
e 2
Hence, the dimensionless parameter becomes:
kt- 4C 2c p-h 3F2R*
Or:
C2h 3F2R*
kt4Cp
The same technique is performed for each of the k - n remaining
variables to produce k - n unique dimensionless parameters.
13
B. Simplification and Physical Significance of Dimensionless Parameters
Once the dimensionless parameters have been developed, it is conven-
ient to write them in terms of some "standard" dimensionless numbers
that have already been defined for specific groupings of variables. These
numbers (such as the Prandtl Number, Reynolds Number, Peclet Number, and
so on) are common to the fields of solid and fluid mechanics and deal
with such phenomena as magneto-fluid dynamics, heat and mass transfer,
viscous flow, viscoelasticity and diffusion. By isolating combinations
of variables in such a manner, the physical significance of each parameter
becomes more readily realized.
In order to illustrate the technique, examine the dimensionless
parameter involving vascular internal diameter, D: hD, which is recog-kt
nized to be the familiar Nusselt number (Nu). Physically, this represents
a ratio of heat transfer by convection to heat transfer by conduction.
Similarly, the dimensionless parameter involving the asymptotic limiting
value of thixotropic fluid shearing stress under constant load (T.):
CT./(kt 3/cph), represents the ratio of heat generated by thixotropic shear
effects to heat dissipated by a combination of convection and conduction
effects. A physical significance can likewise be assigned to each of
the remaining derived parameters (see Table 1).
Hence, by similar technique, a collection of parameters can he
obtained which shows the types of phenomena that are prevalent to cardio-
vascular function. The results of this investigation are presented in
Chapter IV and discussed in the sections that follow.
CHAPTER IV
Tabulated Results of the Analysis
Table I presents the results of a non-dimensional analysis of
cardiovascular function and thermoregulation. It lists each variable,
together with its respective symbol, dimensions, derived dimensionless
parameter, and the physical significance of this parameter. The vari-
ables are grouped according to whether they are related to the blood,
the heart, the vascular system, or to some overall aspect of cardiovas-
cular function and thermoregulation.
By applying the Buckingham Pi Theorem to each variable, a unique
dimensionless parameter was derived involving that variable and a combi-
nation of other thermal and electrical variables. Each derived parameter
has a unique physical significance (column 5 of Table 1) that reflects
the role of the cardiovascular system in thermoregulation. Through the
development of these parameters, thermal, electrical, and mechanical
variables are coupled together in meaningful groupings that provide a
powerful insight into heat transport phenomena, without having to get
involved in tedious mathematical formulations. Depending on the magni-
tude of the individual variables (a subject which was not specifically
addressed in this work) comprising the dimensionless groupings, each
parameter reflects the significance and relative importance of various
electrical and thermal processes involved in thermoregulation. Derived
dimensionless parameters and their corresponding physical significance
are discussed in Chapter V in terms of their relationship to the blood,
14
15
heart, vascular system and overall thermoregulatory response.
In the process of non-dimensionalizing and interpreting the resulting
parameters, a series of fundamental scales associated with electrothermo-
dynamic effects was derived naturally. These results are presented in
Table 2 and include scales for mass, length, time, temperature, and
charge. For each of these physical quantities, a unique scale has been
derived that involves the variables originally chosen as the foundation
for the Buckingham Pi method of non-dimensionalization. The combinations
of these variables, as shown in Table 2, represent fundamental scales
for the various electrical and thermal processes that are associated
with the regulation of body temperature. This is significant in that it
provides the ability to derive a unique dimensionless parameter for any
variable by simply knowing its basic dimensions. For example, the Mass
Density of Blood, Pf, has the dimensions ML- 3. This is rewritten in
terms of the derived scales:
(C/cp)(kt/h)-3 = Ch 3 /c pkt 3
Hence, a unique dimensionless parameter is created for this variable by
forming the ratio of pf to this quantity: pf/(Ch3/Cpkt3). This ensures
a non-dimensional parameter and precludes a longer and more formal anal-
ysis that is required using the Buckingham Pi Theorem. This not only
serves to simplify the task of formulating the parameter itself, but it
also facilitates the analysis of what the parameter represents from a
physical standpoint.
Further expanding on the concept of scales associated with electro-
thermodynamic processes, A series of kinematic, kinetic, thermal, and
16
transport quantities were written in terms of the fundamentally derived
scales. These results are presented in Table 3. Having these quantities
in this form simplifies the task of interpreting each derived parameter.
The physical significance of many of the dimensionless parameters became
evident after identifying groupings of these quantities from within the
parameter itself. In this way, the translation between mathematical
entity and physical phenomenon was realized.
The results of this analysis provide a valuable way to characterize
cardiovascular thermoregulation through the development of a tangible
set of numerical parameters consisting of several thermal and electrical
variables that were selected for the purpose of the non-dimensionaliza-
tion scheme. The resulting parameters may be further written in terms
of more traditional dimensionless numbers, such as those listed in Table
4. These dimensionless numbers are common to the fields of solid and
fluid mechanics and incorporate various heat and mass transport phenomena.
Several of the dimensionless parameters derived in this study were writ-
ten in terms of the traditionally defined numbers. These results are
presented in Table 5. Here, variables having the same basic dimensions
are grouped together for purposes of reference. A sampling of some
variables, along with the resulting combination of dimensionless numbers,
is provided to illustrate that the parameters derived from this study
relate not only to heat and mass transport within the cardiovascular
system, but they reflect even more fundamental concepts of fluid flow
and heat transfer inherent within any dynamic system. Since some of the
variables defined in Reference [13] are inherently dimensionless already,
17
there was no need to involve these variables in any further non-dimen-
sional analysis. They should, however, be recognized as important
controlling factors in the system's attempt to protect itself from tem-
perature extremes and are indeed parameters in and of themselves. A
listing of these dimensionless variables is presented in Table 6.
Moreover, other variables defined in Reference [13] are difficult to
quantify in the non-dimensional sense, but, either from a chemical or
physical standpoint, they enhance or impede the thermoregulatory capacity
of the cardiovascular system. These variables are found in Table 7 and
relate to characteristics of the individual, climate, clothing, concen-
tration and properties of carrier molecules in the blood, diet of the
individual, predilection to cold stress, properties of the myocardial
muscle, statistical parameters, and physical properties of the vascular
system. A combination of some or all of these variables may interact to
control the manner and the efficiency with which the system protects
itself from an assaulting environment. To complete the list of variables,
consideration must be given to the various enzymes, hormones, nutrients,
vitamins, buffering ions, minerals and electrolytes, trace elements,
blood gases, and byproducts of metabolism (Tables 8 - 12) that are found
within the body and whose concentrations directly influence the processes
of heat and mass transport.
CHAPTER V
Discussion of Results
The purpose of this work was to derive the dimensionless parameters,
themselves. To actually calculate them, as well, would have been too
formidable a task, and so this is left for a future study. However,
some general qualitative discussion of the results obtained is in order
at this point. For example, through the derivation of dimensionless
parameters involving blood-related variables, various heat transfer pro-
cesses dre revealed that take place due to the inherent properties of
blood itself. An examination of each derived parameter and its corre-
sponding significance shows that blood has the ability to store heat,
depending on its total thermal capacity, and to distribute this thermal
energy throughout the body via momentum transport, molecular dispersion,
ordinary diffusion, electromotive diffusion, and viscous dissipation.
Each of these processes is incorporated in a respective associated Pi
parameter. The variables involved are mathenatically coupled with the
established set of thermal and electrical variables chosen for the non-
dimensionalization scheme, i.e., Thermal Conductivity of the Blood (kt),
Total Thermal Capacity of the Blood (C), Specific Heat of the Blood at
Constant Pressure (cp), Convection Coefficient of the Blood (film co-
efficient, h), and the Faraday Constant (F).
If one examines the derived non-dimensional parameter involving the
Dynamic Elastic Modulus of Blood (Ed(t)/(kt/cp)) it is possible to
interpret this ratio as the energy per volumetric flow rate of blood
18
19
associated with elastic effects, to the corresponding thermal energy
(conduction) per volumetric flow rate of blood. This represents a ratio
of well-defined physical quantities that relate the ability of the cardio-
vascular system to transport heat by each of these physical mechanisms.
Similarly, the parameter involving the Dynamic Viscous Modulus of Blood
(Ej(t)/(kt/cp)) represents the ratio of heat per volumetric flow rate
associated with viscous dissipation in blood, to that transported by
conduction. Other parameters involve the ratio of energy transported by
molecular dispersion (Eddy Diffusion Coefficient, DE), electromotive
diffusion (Electromotive Diffusion Coefficient, Ds*), and ordinary dif-
fusion (Ordinary Mass Diffusion Coefficient, Ds) to heat transported
by mass and mass flux through electrothermodynamic processes. In addition
to these parameters involving energy and heat transport, a ratio of
heat generated per mass flow rate of blood due to viscous dissipation
and heat transported per mass flow rate of blood through electrothermo-
dynamic processes is revealed in the derived parameter involving the
Kinematic Viscosity of Blood (vf/(kt4 /Ch3 )).
Volume ratios were also derived using other variables. The parameter
involving Total Blood Volume (VB/(kt 3/h3 ) represents the ratio of total
blood volume to a characteristic volume of blood associated with thermo-
dynamic events. Similarly, other non-dimensional volume ratios were
defined for variables associated with other aspects of cardiovascular
thermoregulation, such as End Diastolic Volume (EDV/(kt 3/h3)), End Sys-
tolic Volume (ESV/(kt 3/h3 )), and Stroke Volume (S.V./(kt 3/h3)). Each
of these parameters involves the ratio of the specific heart volume
20
involved to the volume of blood characteristic of thermodynamic events.
Each variable in Table I with dimensions of time creates a unique
parameter that addresses the ratio of the respective time scale associ-
ated with that particular event to the time scale associated with various
thermodynamic processes. These parameters involve such time scales as
the Time Spent in Core (Blood) (tc/(Ch/kt2 )) and the various ECG inter-
vals, such as the Q-R-S Complex Interval (tQRS/(Ch/kt 2 )). Parameters
that involve frequency are merely reciprocals of time scales associated
with the related phenomena. For example, the derived dimensionless
parameter involving the Natural Frequency of the Vascular Wall
(wn/(kt2 /Ch)) represents the ratio of the time scale associated
with diffusion of heat through blood to the time scale associated with
the kinematic translation of the vascular wall.
Variables involving pressure and stress are represented as ratios of
certain energies per unit volume. The derived dimensionless parameter
for Osmotic Pressure (np/(kt 3 /Ccph)), for example, represents the ratio
of potential energy per unit volume associated with molecular kinetic
energy driving mass across the membrane as a result of the existence of
concentration gradients, to potential energy per unit volume associated
with mass transport resulting from thermal gradients.
The examples presented above are not meant to be exhaustive. They
merplv serve to illustrate how one can interpret the physical significance
represented by several types of non-dimensional parameters. Variables
associated with the heart produce dimensionless parameters that reflect
the role of the heart in thermoregulation. Such parameters provide a
21
relationship between the function of the heart-- characterized by various
ECG intervals, pressures, cardiac output, cardiac volumes, heart rate;
and so on-- and the electrical and thermal processes that take place
within the body to control and regulate temperature. Similarly, variables
related to the vascular system are found in parameters that reflect the
role of the vascular system in thermal regulation. Energy per unit volume
associated with elastic storage in vascular tissue, heat per unit volume
associated with viscous dissipation in vascular tissue, energy transported
across membranes by mass flux due to ordinary diffusion, electromotive
diffusion, electromagnetic diffusion, and osmosis, and energy per unit
volume associated with stress in the vascular wall are some of the quan-
tities incorporated in the dimensionless parameters involving the vascular
system.
By applying the techniques of non-dimensionalization to each varia-
ble, a dimensionless parameter is derived that relates this variable to
the overall process of thermoregulation by creating a unique ratio of
identifiable events. The resulting parameter provides a physical quanti-
ty to which a numerical value may be assigned. Depending on the value
thus obtained, one may look, then, for a significant correlation between
the function of the cardiovascular system under consideration and the
mechanisms for controlling temperature within the body.
By examining the values of the derived fundamental reference scales
found in Table 2 (as calculated in Reference [17]), valuable information
is provided in interpreting the relative significance of various heat and
mass transfer events taking place within the cardiovascular system. For
22
example, assuming a normal cardiac rate of 80 cycles per minute, the time
scale for the transport of unsteady inertial phenomena is calculated as
follows: 1/ = 1/2Tf = 1/27r(80) = 0.002 minutes, or, about
0.12 seconds. Similarly, calculating the time scale associated with the
heat transport characteristics of blood, Ch/kt 2, (based on values provided
in Reference [17]) one obtains the following result: Ch/kt 2 =(4.0
Kcalories/°C) (174.96 KCal/C-hr-m2 )/(0.48 KCal/°C-hr-m)2 = 2,975.2 hours,
or about four months! The results of this simple calculation
reveal that the events associated with the transport of blood through the
cardiovascular system occur nearly 100 million times faster than do those
associated with the ability of the fluid to dissipate heat through its
own thermal properties[17]. Therefore, blood, being a poor conductor of
heat, dissipates the heat generated within the body most effectively by
physically carrying that heat through blood flow rather than waiting for
the heat to dissipate by itself through the fluid - a process that would
certainly lead to death since the body would not be able to handle the
heat at the rate that it would be generated. Hence, blood can rapidly
absorb and transport large quantities of heat, but it cannot easily allow
that heat to move within the fluid as a result of thermal gradients
associated with conductive and convective processes.
By also examining the calculated value for the reference temperature
scale, 1.04 x 10-22oC or nearly 00C, one recognizes this as the "standard"
thermodynamic reference temperature for the measurement of most heat
transfer processes. The analysis thus suggests a reference temperature
scale that is more generally associated with standard conditions (00C and
23
atmospheric pressure) than with physiologic conditions (37°C 3nd atmos-
pheric pressure). Similarly, the derived length scale, kt/h, has a
calculated value of 2.75 millimeters. This is on the order of magnitude of
the length of a capillary, the mean radius of a medium sized artery (or
vein), or the average wall thickness of any major blood vessel, such as
the aorta or the vena cava. The naturally derived mass scale, C/cp =
4.35 kilograms, represents a mass scale associated with the heat transport
characteristics of the fluid and is defined to be the total blood mass
divided by the specific heat ratio of the fluid.
Therefore, as a result of this analysis, various fundamental scales
associated with electrothermodynamic processes taking place within the
cardiovascular system were identified and calculated. Through this
process, the response of the cardiovascular system to changes in the body
temperature is better understood and is able to be quantified. Such
quantities may, in turn, be applied to each derived parameter to charac-
terize its importance to overall cardiovascular thermoregulation.
Since the cardiovascular system is extremely complex, as is evident
by the extensive list of variables presented in Tables 1-12, many
experimental limitations are imposed upon any comprehensive study that
might be undertaken. Consequently, the need arises for a more fundamental
approach to determine a working set of parameters that characterize the
system and, from these, to select which factors would be most significant
in future modeling and experimental studies. The power of a non-dimen-
sionalization scheme provides a method for accomplishing this task.
By isolating the thermal, mechanical, and chemical variables associated
24
with the cardiovascular system and by developing from these a set of
non-dimensional parameters, a framework is established for modeling the
heat and mass transport response of the system to a given thermal input.
This analysis has served to develop these working parameters and to iden-
tify the physical quantities that predict and control such a response.
CHAPTER VI
Conclusion
As a result of the non-dimensional analysis described in the prece-
ding chapters, several significant concepts regarding cardiovascular
function and thermoregulation have been developed. Using the technique
of the Buckingham Pi Theorem, a dimensionless parameter was derived for
each isolated variable associated with heat and mass transfer within the
cardiovascular system. This parameter is unique to this variable and
directly couples the related phenomenon to other thermal, mechanical, and
electrical events that take place within the system.
Through the process of non-dimensionalization, a series of fundamen-
tal scales for each of the five basic dimensions was derived naturally
from the resulting parameters. These were identified and quantified in
Table 2. Although they may appear to be quite simplistic at first glance,
they contain powerful information that permits the derivation of any
non-dimensional parameter directly, without having to employ rigorous
calculations necessitated by the Buckingham Pi Theorem. The dimensions
of any selected variable can be written in terms of the derived fundamental
scales. By creating a ratio of the variable to the resulting combination
of fundamental scales, the non-dimensional parameter is immediately formed.
The ability to create dimensionless parameters in this way is highly
significant. The technique ensures that the resulting parameter is non-
dimensional, and it can be performed immediately, without solving any
equations beforehand. It must be reminded, however, that the simplified
25
26
method of non-dimensionalization is possible only because the fundamental
scales were initially derived for the problem - a process that required
the structure and methodology afforded by the Buckingham Pi Theorem.
By examining the quantitative values for the fundamental scales that
resulted from this analysis (Table 2), significant information is obtained
regarding heat and mass transfer within the cardiovascular system. The
value obtained for the fundamental time scale, 4.16 months, appears vast
when compared with the time scale for the transport of unsteady inertial
phenomena - calculated to be about 0.12 seconds. This indicates that the
events associated with the physical transport of blood through the
cardiovascular system occur nearly 100 million times faster than do those
associated with the ability of the fluid to dissipate heat through its
own thermal properties. Blood is shown to be a poor conductor of heat.
Hence, the human organism could not survive if it depended on blood,
alone, to disperse heat due to the thermal properties of its constituents.
There must be another mechanism to enhance heat transport and dissipation,
and this occurs through the physical movement of the blood, or circulation.
The value obtained for the fundamental time scale emphasizes that conduc-
tive heat transfer in the cardiovascular system is much smaller than
that due to bulk flow.
Similarly, the other derived fundamental scales each bring a physical
significance to the analysis through their respective numerical values.
More important than the actual values calculated for these scales is the
comparison between these values and the values associated with other
events occurring within the cardiovascular system. Through such a compar-
27
ison, the relative significance of each event to overall cardiovascular
thermoregulation is established. This type of information must be
known before a more complicated analysis is attempted and, in fact, may
help to develop fundamental assumptions (and simplifications) of the
behavior of the cardiovascular system in its response to a thermal stress.
A non-dimensional analysis was chosen to approach this problem for
the following reasons: First, the technique exploits a very powerful
means for grasping the fundamental features and essential physics of any
given problem before attempting to pursue a more complicated mathematical
formulation. Second, it allows one to identify explicitly the important
parameters that need to be measured when performing experiments that deal
with physiological responses to environmental stresses. (The parameters
are developed through a systematic technique and many parameters, that
otherwise could only be identified through complex differential equations,
are derived with relative ease using a non-dimensional scheme.) Third,
criteria are established that can be used to screen individuals for their
susceptibility to thermal (hot or cold) stress. Fourth, the resulting
non-dimensional parameters may be used as design parameters for the
development of physiologic training maneuvers and acclimatization exerci-
ses, as well as for the fabrication of thermal protection clothing and
gear. And fifth, the parameters allow one to distinguish between first-
order effects and higher-order effects in the analysis of data obtained
from well designed thermal stress experiments.
Given the complexity of the cardiovascular system, it is necessary
to develop a framework for future studies by identifying what parameters
28
are most significant to the analysis. Otherwise, substantial time and
wasted energy may be spent to produce results that are insignificant and
unrelated to the original problem. To whatever extent non-dimensional
techniques may contribute to directing future research, they should be
pursued in a continuing effort to improve the health, comfort, and
understanding of man.
REFERENCES
1. Barenblatt, G.I., Similarity, Self-Similarity, and IntermediateAsymptotics, New York, Consultants Bureau, Chapter 1, pp. 13-30, 1979.
2. Bridgman, P.W., Dimensional Analysis, New Haven, Connecticut, YaleUniversity Press, 1931.
3. Cooney, D.O., Biomedical Engineering Principles, New York, MarcelDekker, Inc., Chapter 5, pp. 93-155, 1976.
4. Eshbach, O.W.(Editor), Handbook of Engineering Fundamentals, NewYork, John Wiley and Sons, Inc., Section 3, pp. 3-01 - 3-45,1936.
5. Holman, J.P., Heat Transfer, New York, McGraw-Hill Book Company,Third Edition, 1972.
6. Huntley, H.E., Dimensional Analysis, New York, Dover Publications,Inc., 1967.
7. Hwang, N.H.C., Gross, D.R., and Oatel, D.J., Quantitative Cardiovas-cular Studies: Clinical and Research Applications of EngineeringPrinciples, Baltimore, MaryTand, University Park ress, pp.
4!51, 1979.
8. Kuchar, N.R., and Ostrach, S., Flows in the Entrance Regions ofCircular Elastic Tubes, Case Western Reserve University, Schoolof Engineering, Division of Fluid, Thermal and AerospaceSciences, FTAS/TR-65-3, June 1965.
9. Land, N.S., A Compilation of Nondimensional Numbers, Washington, D.C.,National Aeronautics and Space Administration, 1972.
10. Li, J. K-J., Fich, S., and Welkowitz, W., "Similarity Analysis ofMammalian Hemodynamics," in Welkowitz, W. (Editor),Proceedings of the Ninth Northeast Conference on Bioengineering,ew York, Pergamon Press, pp. 50--53,181
11. McComis, W., Charm, S., and Kurland, G., "Dimensional Analysis ofPulsating Flow - - An Introduction," in Copley, A.L. (Editor),Proceedings of the Fourth International Congress on Rheology,New York, Interscience Publishers, pp. 231-242, 1965.
12. Schepartz, B., Dimensional Analysis in the Biomedical Sciences,Springfield, Illinois, Charles C. Thomas, 1980.
13. Schneck, D.J., A Non-Dimensional Analysis of Cardiovascular Response
29
30
To Cold Stress: Part 1, Identification of Physical Param-eters ht Govern he Thermoregulatory Function of theCardiovascular System, Naval Medical Research InstituteTechnical Information Service, Technical Report Number NMRI83-51, NTIS Accession Number AD-A138 710/9, September, 1983.
14. Schneck, D. J., Biomechanics of Striated Skeletal Muscle, SantaBarbara, California, Kinko's Professor Publishing Service, 1986.
15. Schneck, D.J., Principles of Mass Transport Across BiologicalMembranes, Virginia Polytechnic Institute and State University,College of Engineering, Department of Engineering Science andMechanics, Technical Report Number VPI-E-83-07, March 1983.
16. Schneck, D. J., "Pulsatile Blood Flow in a Diverging CircularChannel," Ph.D. Dissertation, Cleveland, Ohio, Case WesternReserve University, 1973.
17. Schneck, D.J., and Starowicz, S., "A Non-Dimensional Approach tothe Analysis of the Heat-Transport Characteristics of Whole HumanBlood," Paper submitted for publication, 1986.
18. Weast, R.C. (Editor), CRC Handbook of Chemistry and Physics, 52ndedition, Cleveland, Ohio, The Chemical Rubber Company, pp. F-266-F-283, 1971.
Appendix
31
a) 0
.4-) -C 0 a)QJ WO(L 0410 4-J 4--) 4-)0
V0 0 m .- 0) c0 a)LAJ< ~ 0 ULC) ^ 0-a -- 4- 04- Ln t-- 'to
0) m 0 (n LU CA0 a1) u
- 4 4-) a) V-) L. nL 0L IVuU 0202 02*, >) Lrc DLn :
- - : ~ 0 2-- U E-c E 4-j L. =
C-1 a) C (Acn C CL -0 a) CL0. La) 00< 0 no 00u 0 0- E Lf-~ L-) 4-.- u. >.- ::-00 02
0 0) CL L -04-'
=) 4--) U L- E0 .i-D0
-r WL O UW 4-) ai X0 - 0 U -
>- aL)2~ 02 LnCm U43O-C a)~ I- 0
a)a)V
4-r 4-) 2~
C 0C 02..-C a) -C 04-) LLU LJLL~ .I (0~ ~4-
.: - -. .J 4--)S-0Ca- uji - m -1Z C. u
>C> UJ ri- 0.. uC?) LJ .. 8 .
-i M LU -:t-C 4-' 4-'
C)
C)uLJ - C\
o o
0V C.*)i2o
=3
4U-0L -J
co c<X 0 - 4-8
0!A L -j 4-
4- u C)4a
> - c 0
4- 02-'0 L
Q 4--C 4 )
UU L-' 0 2
V)-
0 4- 00
4-.
o0 4--- 0Y ko aA CU 00c
(u CC 0 - :Cu (31 (K3 "0 4-) 0 -
L . a)(LC- CC 0 -.
ro 4--)
E a 0 a CL C) (a).. L. 0 0 u-'~ u -m 0E
- - 0)a C -C -0cu C) :-*. -0 :
-L 4-) tm. (A C > - Q E -4-
~~:4- E- CU CL/W
m- (1) Ln cuL (0. -W E a)0L) uaU 4 LJ a) CL= .- c) Ca. 0 4 ' 0-Cf CW ( - _c- (0
. V.-- I U m- ( C
4-. 10 C) a c U wU0 4- CULWV0 WUA L--C c 0 Q. C o L
cn OfL/UQ L ->(A U 0 LCUO Lj Lr-
4-3
Vd)
_ i ~J ui 4-J
- Z LUL- U0 N~ CCU M:L U0 -le
c w- C) :c -...- L = OfCu L-j m4-
4-3 0m LU 4-)C-le)
-4 CD.
LUJ-jCC L/)
2- C4Ct) I
0 I-I
4-
Co ) (o 4- 1'- >3 0 e
E i -J4-
o CC --
Of ) 0
CL (1- 4 C C)
c CU C: 4) 4 4-
-4-u4. (l Cl >C
< 0 0 (A >,J ::-
co no L0 V)cU0L
C CC 4)r() -) 33
C0 V 00 L (V
WO) m C,0 a)* a)~ c ui);L. CX L -)-e4- - CD' - C
Li CU( 0 mi (A C C ) L 00
V) ej ci (a (0 n3: 0(f 3: 0 Cn .(
LL.. LLU 0 .4 a-- C.- E
~ 4-3 J >) L)U.A aL )CCD *~(A c L. CL 0- L>)- e 0 m~ 0- 0 a)
L') a- .'- 0.i 4J -C _0 M C-0) Lii L 4 -) C LA LQ a EE 4-) U 4- 4--) 4- -1 ~L
cz ai 0)5 0 LL. 00 a) L a) a;C )- E - c( E u E> 0
- 0-.- =C c a=(A =3 m 0.7-0 L3:) u~ c U) C 0
DL) 0 >. 0 0 CO 0.>,a 0 (D0 re- mn Xl
a) 0 . ) -)0 Ci- L
>,-0C-- 0 rd D 0- C - >0 ICM~U- c) 0 E (A i
L0~ C" L L- 4-- 0 JC LW 4- 0a) L M 0 0 ( a~) 0 (Z(I -) (a
CC: ) O a c, a) W4-- a)L C o CU )4.-
C .i Lii
C)- LiiZ J 0. CL 4) ~4-) CLUJ <ii Nd -uLi -se 4-'C -9-00 -
o)
-4
-LJ
- -
CD I- -Id - - -
V)
CD 4-)4-
Lii>- Li Lii CZ)
Cry
LC 0)(A0 aj (
-- 4-() 4-
01 0 0 0L) U 0C C
414U - u
0-. CL 00
cCC 'U C:-(A(
~0 m- 0 '4-
00 U'.-3 0
0
~ (0
'4-
4- (4-)
L- UA4-
LUJ (> C) (C 4-) QWL) U- C 0) a) W to >
.- 4-) t- 4-C) 0I O
4-W) WE 4.- L CL 4-)a)- EL EL C) - -
L- E4. c- Ei L-j 0i VC Li-
-U - Cn Wn - v-C-0 ( 0W -) L. M c L-C Ln W 4-
:. >- 0C =3 u( (u WC C)0Gl LU L 4-) m i (n( D 0u -- >< L V L - , a) ai -4-3 '!EW u -t1r
.4 -C00 L E 4) (OC Q- 'a- .rV) a .~ a)W a) L 4 - =U LC) c0
L. ai. 0( u, j WL L. U
0-- 0-0 cL E -W L.. 0.U. a)i ) L Wn L. (0 -:t WC- C) 0 c M.1 C
> 0- M-. - ~ 0- 73 L CD 0U W) L- LL- CO - L n ai C) W.. cL0) L. )
0.- 0.-0 C V *) U L0 W mEca-- -4-C) u Ln Wc 4-' C)C a)D (0.L43
V) .z C) I - U0 0.> n E0t0- a) 0- 0. LC a)t LC) L o 4-,
f -3 m~ 0 ~ 4- ro~ rEC)0 C C40 WO a) 4.3 1--,
Wo C)( - - Wu- CfC) I
N) LUCn~
C - sO C) W1 C-u M0 (0W 4C--) L4 L L W(A W'- WU - C- C)
0 =LU <)r
WC)).iU-~0
C C LU I U 4-l C)'-
C ~ -~ 4-C) C)W4- - -
V)
Ca)
Ca)
LI OJ -)
-- 4 ) L
CCC) V- ,
'4--
OfL C C
4-) : 0 C)
CCC) (0 4-
LUi '4- E -a
u- w U C) La) Wi C C: V
cj > *,- 0 .- *.-rLL LA-- C) -C ) 4-'
35
0
4-)
4- co 4) 4-)
4- 0 La, 0 L 0
S4-) U -a: 4-) 4-3a
4a) A (~L
*L L- L C0 C. 0V
Z -J 1 L C C L 0 A ( 1 IA
Ln U)DV) > co wA L0 0Ln u)~ 0. CC n C7 a, 0
LL O IA CO tn C-L ) 0 ,L) 4-*- rAW a)> 0) ) - ci(V 4-A EAI C 0')- 0
(D CL- Ln C4-I 0' CA u C(
- CD a,L -0)-- EL. C -a, eu 4- a,Le) -0 CL I Cl - o: - C CU a, CV u
a)>1ai0 - CI C-j 4 - ) L 0 CE C U aL.G WL
L Dc 4--2 E ' C) C 0C _ C- LO Ca, 4-'( C 0 - C
V) 0- It C l >, *- c - W .- CC- CL (a- ZO C>3 -0 r4- >, co
c dO IAV LU) I 0 Ia -- a
C-c 0 L. C L-I~, C t-W 4 ,
c) a- LC 0,L CL CLa a
0) L- j= E L- 2 L-
c 0 d mQ)4- (a r- I4-( M 4-rI0C - a)>) C .- , a,-, C a, C) aC)
_0 V)
- LJ 2- L U4-1 C) WL 4n L) co. ~
C -~ ca ~. -czr m LiJ mC )A 4-) -- ,.- C-- -)
U LU 41
M)U
LU _ _ _ ___ _ _ _
>- CY C,
CC)
C):
0C
C:D C
(0 4--
ea L- -uW 0C
- - C) 0
aC/ C:
C (.:)rC
36
4-3
4-)
4- x< - 4-0 0 -
- V)
C e LL. - <co LL 0
3) 0 0)WO4- a 4- 4-' _C-- - - _4- LW4- ra4) - 0
LIJ4-) G4 -- L > )W a) -(. D V 4-J cc>C) ) CL
u 4-) 4- a) En 4-') 4-) -0 O04- 4-c (n- a C.) 0
0 ~ - -0 -0 c C=u( Q) () a) a ) (A 0)a) co t ro c- 4-) 4-' E E W a, 4) -- (V uL) ro ru to0 c L )
0 0 *.- u ' 0WO) -L- r
rO 0 0 c- 0- 0 L 4 j C-0~ U U) ( UCO (A)
- U)C Le) 4-) U) 4-'- U) U) 0) 3 CL/) 0 C *'c 4-3 z *-0- -VC
0 u CE a~ C4- EC ,- a) a) a)a = W4 . LO Lo~.CO - 4- -O 0 (U) u ,
ma Lo-- L ) ccL C- 4-'0U.. Ur u U W0J V C u.C U -C .O I--
L)c LI ) 0. - L) F- L) C ) ):30
a) 0 ) 4-3M (V 4-3 Wa 0 LO 0co (VEL E ra, ei Eo( ELc a WL) -
c) -r a~ .- a cu j C --4-) C 0
-O - L
CD Lr-l
*. L U - .E: VU --o
0 Of L") < 4-3 p m. . .. ~m LLJ ~-
LLI)
CD c
4- -
-4-
(/))
0
4- 0 4-
C0f C ) U
i o L
-. 4- U) C -
.41 cC- a,L 4-)V
0J 0
C ci U) 3
CJ Or (a Ca U -
c n LI) z- L/) 1I
37?
0
(1 0 1) c
E E :- 0 0 :r04LJ ., ) a) mW.L
o 4- L C4- 4- Ea CI- L ) C
0 m~Q C u cW W aW
E o LL 4J ( cC a) c- cW VW cu "o L. - L
a) 0i- ei.4 Of L- Lk W= 0 WQ -L0 C V) V) - C
ai 0e ec 0. (W co L OW 4-
4-CL 4-- MA- a 4- CD~-
Ln W0 t- (a o L&- 4- WC W>- o. ) 'aC ~-W C LL-
4-C WtV eaL C3 aL w- - CW 4-3- 0 C-- 4-j ' C 3: - '
ci E o i 0 (A ( c fu ca) Eif c4 ' t-W Wa) Wbo.a)
>- o *e L.- L) L j L(V C- 4-W C. c_ ai W - *L W)
A. 3 - V.). ro0 m-. E~ 4-- eo E -a)v We- a 4a' -- (V Cj --
C- LUJ Ct 0 W L
0* 4-0 rOC IvE -I-u LL- = ~ F- co >- 0-C
C D C) LL C-) IL u
Of VU)A Lo-> C -
- L - o-f-
.- 4 0~ V) ~I2i-
LI) Ji <D;;_ - 4' C4(0LUI
-JL
C)
E- LU)4-
4-4-
0 0 0CC
J~G > -)CCC
< - .n -C
D - L LW
C- O W - C- 4 J 4-
W) L W W0- L >
38
a) u 4-'
Ln4--
0n 4-0
0L Ln
0 toLL- 3-: 0
F- 4- >c
LI 4- ' *a--) -' 4-C>a) C L C- E. 0.
4--) L(0 W L n-D L
V) (V 0) cc - ::'--:*
2L Wuo cccE c0 E3:I 0 V 0 - L- 0 L- C
C~ 4J = 0 CC (0 a 0 0i
3:) W/- Ur1) Ln C: >r Cr
>- 0 (n 0 ) EE EE-4-)4- -)> (
(10 F- 0
L3- L/)L/e /I 1
4-)( LJ 4 - =*- *F, 00 O
u (-. C1
C UJO <
L LU
-41
-J-
C-
I4-V) CL
4-3N
LU 4- CI-4
C:
LLJ C 4-)4-)
*C.J U0-E
E - EC/- 0.a - c
F- F- F
C--- 39
eo >1
E 0 0
0L a)-- c 0 0
C: L) L)
LA. 1 kC 0 0
m- 4- a) 0 (4- 0 4-(VJ 4-) -v3 010 4
a- 01 4-) L)C
-: E 0L -- 0 . 0 0a-. V101 ( 4. 4-' 4-') 4-')
L- =5- (3< . (In 3 .
- 4- cm C)0
-~~ a)- E 41. 4- -. ))-V(C1: v (0- (0 ro _0
0 4--i (u- - 0 .- ~.-O *. .--- I ea MV OE- 0 L- L 0 00 0~ w >.- CL 0 0o- 0 0o-
tn CA EO I-(M( ( n (COL/-3 U- U- *,A Ln V)- ' <.
>- 0 0i O0lC:D> ::D u 1 c 1u 01) =
C-. cu a)C C: r-0 - >, 04-3 eu ru L.. (V LV . (a L.
(V (V 01c, u1 . 01 0.
-0 0 E 001 a 010 a) ,.-) L. a) 14-) a).. CJ14-'E EQ -- (a O E E(Vo EL E r
C k- a). _r_ . a)0 *01 CU
4.1 CD w4-
0 aC (/') rnr *0
U LU ;_- = 4-) .. **
LUj-i
C)
C)
4-' 4-.' (V4-'
C')
~00) 0
>c4 (V 0
C') 0 01)LUJ *'-C CL
-1 ( 4-.'
- 4- -0 04-) 4-3
0- 0-.(V C') (f) "LE It0
031 E L
-. 0 4)
4-)
4- -) -4-) U 0
4JC 4- V)C
- 4-' X
LUJ
0 4)JJ a
_0 4-3 c
Ca Q) u 0 a
C-) L( 00ua) 00) 0) - C 4-- -'0 ,-
LL- 00 cc I - o0 -~ a:- ~ ,0 4- L E r
col 4-4-~ 0- U..
0.C 0*,-C Q
V/) a) 0 L. >1C F- 4-) >Z ~ ( 0 *-E c 4- 4
-. ()L-- L-
.J =3 ai 4.- E- E0C 4-)
- E. 0nU4-) :3 4-' (v
0 =3 0 C 0V(A 0 .-- (v/ E=3 > . 0 ::3
>- -:'~ . 0 >*: .c 0
V 00 L 4 - 0 ~4-)0 0 Q) 4-- C4 C0 L)A.
- Un M, 0- m-0 :3a.)cn Ca) 4-' fo d)( a)0
ai cu u 0 a) L >, LUO CL C.- L 0) C) 4-) U c m .- 0
a) 0)C 0O C> L Ln .0 U-4-) 4- 4-3 (0 (na) caa 04) a0 a) .- _ ):_ (U Cr- a) >1
ce 3:C~ L)IM I- J.0
VI)
LU0Z
:3 LU I- - 0-CD > ~u i 4-) U)
4j~ V~() c > 4-) mVC m ' 0L 4-
C L -' 4-) U .
LU Ct)<
CO C)
F- V~')
LU m
C)4-
M>IC LU LLUJ
C),
0= 0
0 4-3
(0 C 0) a
LUi E 0._ 4-') 0- 0Ji Z3 C E LA
co - 0. .- 0 (A
'a 0 4-
0CU ( a) :E
cc 4-) =5a) 4-) a
(a a 0 0 C: C.4-' 4-') -L mA C E0 0 (D~ 4-J (10
41
14.J 4-) 4-)
0-
=3 U
0- LlA 0-A
4-> M5 . a).- aZ( _c--
3) (
_0,' WLJ OEAj EWJ
u A Z: U
4-> cf CE-
C-0L1 C) C
L/A)
C w~o 4-- -
V)
-42
4-) 0
C I U
CU C4C.
C .) :3 cLU r(n (0 4o C4- 0
43 r-u- >, 0 --
cz 00- L- 04co) -,: (1 0 E= -C .-n - - 4-) 40 4-)
I.J .< - 0 .- 0111 0 t
0- 0- 4-L
- :34i :.:D Q) (V (V0
j j >'nr *- -.-
C'C (I 0 0C,2 vi Qc 0) tJn~O 04) 2
C .- ~ (A aj~f cf4L 'o a U cai (v m .- u a Er- 0
: C CL (3) CO) Q)a) .- C
7U C.L Q)W)0 00 O . .-j .C ' 0 UL
.0 L- -7o -
ccO WW) I'0 - e
C,)
C,)
>0.L >1 4-L
4-)a) 0 0 u
0 LU2:n
C- V
<U LL
-D -H-3r
2:C 0 H
-J.
43
Ci Ln c 4-
5S) 0 0 0 0.- 0(n c CL Ca
C/i (In 0 C: c (1) C:W)' 00 ) 0
4- 4-3- u/ n <
a) CL ,-CL :3 =3
u.J E - 4-LC 4L) ) LL 0C c 0 4-) 4)
E S D W) L0 Q. C) m -c) <LI C)4-- - a)
L) - n .4-)O 4--
U-_0 'a 4j to 4- 0, .
-4- .- a) 0) W) Q) 4a)d4-) L 4-)0 - I 4-)' 4- 4 -)a)o OW U)~ ma "o'0 ( a
a) 0CC 0 CL0 0 0L)0 SC 0 a) 0~- 0 0 00
-' 0 Z.,.j L. ::- L CO Ln C .1 (A L. L- u
0' 4-0 oI a 400 0
a) (o =0 Wra 4-> U WW- a)) u- C -0 .- N cc 0 a) 3
0~~~ -~ 0L 0o a,-rL
ro Lo L- M. L--rai c o 4)- U) 4 u =O u) 4 C UW'
c- (DI _) cI c e 50. Era mI C L/ 'a00)0CJ0 a)u "--a *,-a .- ) ~ ) *-4.-) C -
0a) a LU- -i- C-I N - a>C)UJ cc -D 4-ce -
C .CDLU 4-) C) )
Cy -1
c C- < -
0 M CL
CD
-J
CDr
CyC
0
4-)Ma 4-.)
4-) C E
co 0 L- L-- I0 C:
I: In 4-)< 4- -aa
> La)c ( a) mC
Q3 0- M )
CaC
0
0
44
o0 0 0C
0 0 u 0 a) 0a)
o 0 Lu :4-- 1- - 4-
LUJ 4-LUa 4- ()= 4-u. 4-) 4-) *-L- , I
C:) 0- 0- CD ~- 4--) 4-) ) 4- 4-1 4-) 4 -) 4-)
LL. -.
.- a.- aWa* a) Q, a) W, a4)(3:f 400 4-0 4-J (0 (0 0
U ai u00 u0 0 u 0 0 u 0J0-0 0.- 0c 0.- 0 0- 0 0.-
0 0n (A o 0 L (nO tnE C, CC0 0 (1 aV)~ (,) C,) 0, LO LnC
0)CF 0)CL a' eu (1 Z a) fu 1)~ a, aU a,
.- 0 - r- - 0 r- - 0 -0(0 v C0L to~ 'OC (0I (0L e ~ (
00 u U u00 0.Q U 0.0- (
LU 4L ) - U 40a 1 a a 4) a (U :E c E ( E c Ev Eco EO E.4-j E c
.W *.a) -a) w.a 0)a - a) -c -a,
C c - i Li.)a, 1 LiJ.P- N' N -4
C -- M: = e 0 4 LU .Jof 0 C)) 0- -. 0- Lnt ~ 0
c M LUJ~ LU U)L) U
0 - -
LAJ CI-)
C)co I- of, I .,
CI- CU
> 4-) 4--)C')
> 0
4-) > a,LUJ c L.0 L.-J - a, a,-
4-4-3
a) (0 -~C) (m0
1 4--) 4-)0:: a,
L. 11 1CL. CL .-
J4-5
4-) 4-) 0 0 0Z3 0
CL~ LLUI 0 0 4- c a) 4-W0) 4-
C) tL (I WL J- LU (n
a- C C CD C-
- 4-)r 4-) 4-) 4-3 4- 4-) 4 . e I-LL *-
4-)4- -0'"
(3) ~cn 0 0 0 0 0 0 w 0V- 4-) - 3 4-) 4)- 0 (j4-) 0 3
eo. WCL Wa M' WM WW- C 11.- (n CL .- co - .C: .- cc.-
cr U W 4- UL u ~ UW U' U 0) usC ./)W 0 ( Ieo 0(.( 0.10 0 Cg-- '0 ;1J>C 1)0
<C 0 _(z 0l 0
- c JY LU
0) -C a) co 44 . C C ai (3.) 0--
-. ~ ~ ) -- N 4- - - -. 0 -
1). (1) > )c C) V / v V C) U )cW - U C c a 0LU ) ( -) Q c C -0 a
c -4- 4- C-F- LU-
-jV)A
(0 LLLli ;2_ F--4-'
:: CD L.-,4- -)0
c> LUL-c0(
LLJ C )
LLLW
CfC-- C f C
4.J 4-) 4J 4-
4-)
.0 -0 CC 0 C 0 0
0 0l (1) 0) *- 0na)m 3n0e ) C ) L 5
wL 4-, V- (1 4-L) - =
On C- 0 D 4-J 0 .-
4U-1 4- &j) 4- 04- 0M 4-3 41t 4-3LA- - - -. - (0 - - N *-
C.) i 0 43 C- (3 W0 Q)- w 0- - - 0 4-) 4-) 0 4 4-) 4-)(0 4-.)
U co L/-
-.) 0 0) )0 0)i O0)0 0) ~ 00Ln (0- U 4- (n0- ul0 (0 -L- LoC0DnL- 0-
L -C (n *.-C -.- > 0'C *.-0 V*.-aCDLnM L< 0 0 0 OD/ 00 0
C)~a 0 a)0 0 0
F- F- F- -
ro.- ro 0M0(4)0 (~ (
0u U 4-) ) 0 0(0 > Q 04-)Ln)> V)/ca 0 I (/1( () -Q (/1 M L/C: V/) r
. a) (03 a) .. r.-- <) 0) 0)
a)C (D ( 0) a)-*c .- -10 cu4 Q-4 -4D
'I-- OfC o~ 0 "-(C -D 10 0-
'C CD j uja) L U M 4-' 4-
>~L -_ 4 ~4_) 4j4
af V)< ) .. 4-)4-) uzL c =. Of 4-) o
C CLu C C-)
0 -
C,)7- I- - F--H
-LJ
>- 4-) 44- 4-)
(/0
00
> 7-W0 > E0
4-'-4C: >) 4-
0 aii
4-U > M -
> G) 400) (0- >
I
47
c 4-
0 0
0 4-- c C0 ea3 0 :3 0 0
0- cc(03 '4 4-J '4 4--LUj 4- E 4- C: 4- > 4--
C0 c0 (L)-) 0- r =
4- 4)( 434-3 4- 0 4-',
- -C 3 3 -- t eo 3-'Z- 0 C- Ct-D 7:; c0 m:3 - 0 0 0
C ) 00 W-~ U 1 d) 00 Cl 00Vt) 0) 4-4 0 4-0- 4j- 4-) 4-) 0 41 0
cc (0 C0 IVL '0 '0. 0 - r.- coGW4-) - .- 0 cc-0
a< u) Q 0C a 0 0 0)_0 -D OC 0 a) 0- 0 0= a) 0.c-o Lo C7, (A3C c- CAC c Cn " L (10
C/3 2- (/) =3 (Ie u0 Lf uZ: /
>::c0 -:30 C c . 0 V CL- :D WC 0 0 On( 4-- L-
0)
m G) a)L uO v0, Z3 W(0- j-
U- 4 04-- . O- 0 c U u4-) 0 04-
c0 a 0C C) 0)01 (1) 0 )0 WE) _- ) CL
E 'E E- E E E
(/3 0 I0~ cc 2 c HC
LU)LU J LU
0) L U = C1 1N C=3 LUJ 4-3 4-- 4-) 4-)
- Lj C 7-1 C! 4-) _c_ .0C n L < C-) C )
0 -
LU/
co LU
2- < -
CDcc
40- 4--
V))
rLU 0 (-7 i> 0)
-j (2 >)0o 4-, 4-'
C7 C >
>3 0)
C F---E
(/3 U') F- -
48
o 3) 0 0 0
:3 :34- 4- 4-) 14-4-' -
W -L J 4- c 4-
(0 (0
0) Q) 0 ~ (1 (3 C a) a) >) .0)V) 0 4-3 0 4-) 4-) 0- 4-) 4-) V) 4-)
M - 1 o - (0 eo
-1 co zC - C-c Cn CO-~ ~~ ~~~ 0u) ) 00 0 ) )- 00
(A u ::Io 4-.) =3) L/) Z) o-( =.
<0 ( 0 0 -:3 0 0(0 0
- ~ ~ F 4-0J~0 ,~(A ) 0 z -co. ~
0) (-0 (0)0 (0 (00 u0 E u0co ro( (A ro( (A0 L/)(0 ( - L. n r
0 u a) L ) 4-..' 0 4-)
C. E- E Eto E a0) E4-3 -4- *.14 4- ..- -4
0) J C..J
= ZA- NN 4-1C D > LJ 4)4-3 40 (A
cl (A < (0 -4- 4-j -' .C ULJ = 4-) -C -C. C-0 cn < (-.3 -::c uuc.0
(A
en
C
-j
C)
-Q 4-1
-4-- a)'
0-0>(00.
-i (A 0) 0)co ) D - Q)
0r 0 O
a- ) CLE0 E
0 (0*, 0'w 4 - ,z
~J 0) C49
0
0
C: 'c c c0 a) 0) 0 *-0 *L
4-' -L .(0 (0 0 c <C
:3 .-- In :0 4-- L. 4- L
UJ) W 4- 0 0 4- 43)0 4-- -~ C
0 0U L C 4-) CCDI 0 0 ) _0 (A0) c 4-) C
-:c 0 a) 0 CC (V C 3)c-L Cn -- -0 L 4--) .4-j() 4) 4)
U. 0 00W CC) 0J 11 .- L *
- 4-t- 00 C0 :0 :3:2- 4-) 0 r-0 4- -0 C 4-CD237 0 V CO ~ L 0 ~L Cr -z -0e (a ' C
W G) (D0 0) 0 ) 0 0C _a 0D ((/ ) . O E 4- 0). 4 .0 4-)0U 4-- 4 -)z
UJ 0r CL- 0 CL- ( -~ (030) '0 0 >1-Io- - a) 2' a) *-o U- - -
u 0 0 u (V~ 04- 0 u ODC0)(0 0C Eu 0 E ke 0 _c- 00 0- 0 0)
- t'n0 =3C = C: L IA0( u'(n o (0OL
LnL D V)3- (a - >- L V) :3 A LV)
CL 0 a) ~ a) co a):3 )Lj
C) 0 r (0 c0) mt V0) 0 (.n - 0a) CD Ln (3 L0)
k- E 4-4-) 4- 4-) 8 - EE4--0) -4-- C 0) - C: 0) .- *.-4 m Z:-j -C LUJ a ~3 LUI Of I- I:I-
0 W Of
I-= --
of c3 -r 4-) - ) LUj 4-) 4- 4-- 4- 4-)C u = LUJ 4
LUi-J
(/o
WU UJ 4- 4
4-'4- G)
0)8)
C;
Cn (1 ( - J0
0)0 LnLL
Of u 0< 0 4 Z )
AC )40) 04)
C: LL m 00 n
(, 100- CC
0i 0
50-
4-) 0 -)4) .
-0 00. 0 LLco 0U 0)D 0
E 4--3 0-4-W G W co ar 0 Ln00 Ln ol n- c.
4-)-- 4 L- LU -D(0
> ) 0) a. c- 0cLU4 >D We (V. 4- (1 >
C -) - ELv- (n Ia)
< 0 ,- - ti cOU ( 0L-) CL u 0~- L .( LUJ '-(A
- ".- >WH (i - 4-3 co (A n0LL- >.,- L- V) 4- (
-: C 0 4 - ) 4-)(~ En (4 LWa 4-(A= c-0 .- a) 0 (4- G) 73- 00
::- D) Wn 4--W L) 0, (Ln LAJ W ) W- 4-4 W 0)0 C
0-) LU 0 - CO 0(4. 0)j fE ., :Lu 4- LOL 00( 0 .L> a) 0.
.-. a) (4- WOO - ~ 4- U t 0
4--) =3 J coO(A 4.0 4- C >)::
V 4-3 0) (AW a) - 4 ELn 0 a0) (a 4- 4.A U .0 4-(C
- -C. WO -0 L 0 0 u 3 -02 LU F- 4-) eo( ( L - - ~ =3 c >
c. C 0 40) 0):. c)0 (D L-i C040 V), -o L0 0- 0)0 ) 0-
c > '4- U WD E 0 ai -0L 0a0 )W0 c0)W -- 0 V)4- = (D (a IV-( C0.)0) E ) 0) -j0 FA 4d-) a3U )C::3L 0: (t V) u30 .- L a) 0LQ -(0 - 0O (L ) (A V (o X O 4-30 Ln( (0
04- C 0 L- M( m CL (0M c (0- 0( 0 )>
V-)
:3 L U: - u _9_ (A u
O L 2- 4-)C. > 4-)
CD
C,)
U 2- c'J-- H
Ct) f I -
H-J -i -
LU n
CD i
E > E2) E
Cr)Y
0
00
U V)
0 4-3
Oo E
OK 4-.4)
-I 00
t4 (0V) U X a
cu Uo L0(0: c--
L 0) ),-51
I) 0
4- 4- A- 0
L1 0 -
L 4-) C-L
L CL C:
0. CC 0 4-) L 0 c 0 u0
(n aC C (n, L- - (j Z
0- - E - - VI L- - t , 4-.C.D W-.- 0a (vC CG) =3L 0 ( 0 3 C, 4-- G 1- E E u E (n -1 u C0 .
.:I a) >a- M: -- -Q C:. - SO. - c
c- C CL) ca 00L 0Q L- a)- 4-'LLJ 4-rC .- ::. - 4- C 0' -'- I.
ED4- .-- C m.~ 0 C C>- CW C -C ai u--- ~ '
=34J C> =
0 ~ a) a) cn_ i D0 11 -
a) 'u LE L-, LE CJ)424 LE -L .-) a L aL1 . L- aL- '0 .~- 0LW >v >DC >,.- eo , C-I ) (- (
C~ 0 U u'C 0)~ULCc1 4,- LOL -- LCJ 0 ~ a,
aia, a >1 c, 0 cC)> C n(
uJ>e 2Z LJ<W rl L of
Vt)
C: JW C CM~-i 0 C- c- 0 0
C CD(U CL 0 - .- u C u- ~0 - 7: (v E u~ .- - -
U (-n' < - mv -- E mm
M: a- CLa V
-J
Vt)
-. H
LU
C
C) E
co' 0~
0-~
V) CL0 C-
71--
cc -
wL Lr+ ~ Lu-1 4)4J 4a, 0,a C
col C C-0 4-) 4--)-C
- 00
,L CL 7a-
V) Cl- -
C 0
~~0 a-C.0~0
52
a) L 4-
a, -C
0- a, 0
wA 4-- Co-
C) '4- C -
Cd co 0 a) 0 (2) 0U- -i -C.-a A~,C L -
I, 4-) 4-) (A 4- ~ , LU C a
CDaLu Ca, 'V C:-~~ <e -o>-, - 0
Ln a, a, Vl W 0 ..4-) 4-' - E E L V) 4-) V)
-J 1'V0 M 0 'V CD(2 Z3 0- -- a,< .- C0 :- E c - 14.0 -C-> u0 U 0.., Cu 0C 0 4
- C. 4- X L(- 0'. - 0 -
(f): cA) eo- D
2) a,.C CO- -- ) 'V 'V
a~ 4- ,C- 4~-) -I J 4.-' a, ro a, 0 (
CC -' .- ' a C> oE a- (
>LOC CLO. 'V , 'C- Of -C -L -Z7
c, - a,.. 4-'4 x-I ca-V a, L7 a
. L U = ..CmC- CD JLJ E< C
L/- <C 4- c U
u LU = t 4-3 (n) A-) r
- CLU< -:c 0.4
LUI
I I-
F--
C)
cc CD
CLC
4-)-
fa,
44--
L C7
0-
C< 4-)
0- a,
(uCL
53
L 0 1
ro L1 (V >)
DA E *- (A u2 cCA 42 ( (V 0)- 0-0
0)) L:: EW E
L) L4 CT) a)Ln = =3 L- Ca) 0
LL (I - o 0 l 4- 4) (V E (A L)C) 0c V) 00 - 0)
QO 43 (A o A <v~ 0 ) -
0) EA L. -) o 4-)0 U 0)E A- 0 *- L *.- i_-.a- to *.- ZD
c > ~ ( u u- L) CO( -0t
(!2 0) 04 00- a) Q- 0 C -a) CD 4- M Ln :3 L0 eo m (asj 0LA .- c) :c0 0)00) 0) L)- C~ a -
CL CC EL 42 c > c 04e2 E C- C(J OLC O - (V-a) c (0( uL -a -C)
c) Lo 0 (A0 .A-L (A 0-) 4 0.C 0. 04> 0 c (Ve (A- L(EA04-O E (o e 0(
S L. 4-. <0 L- '- C (0) >\( 4- -- V
Cl : CLa ) r V)0U a 0 a)Lc
) 1-- 0) 'V E Ee a)v-C4-) )L U2 v 4--) - a )C C )- a 4-0) UC =3
0D)20 (Z E E L 1- 4- 4-3 42 0 4-2 -C .- Q0. a) > eo4 COLe ev- e -- 0>, C
-jUJ ~ CN
J CD C-)0) L/)A <r CL 4- C4 -
U- C) U Of(~C M- o.J <r -. o.' '
ujNZ4 -)4
0i E- I2
U]LL IZ -
- I
no CA H-D
Q )"
E 0 C;E-43r>- C- c4-,
U) LLL
-- 0
- C-- LL 1
4-c) L Co
(L C: 0-
Ln 4J (a~L ) 0 0)
V) 0 v0-) 0.-0
It Ua -- C42 C
Ll 0 ev- a- Cl
0- (A 4-54
4-J
C) 04) 4
L-o -oc -
>1 0- a) C ai.0E 4- C
LU~~( 440)a U4- 0
e) (1(0 4-3 S_ C 4-- E
CL) CC 0. C-) C cz a.. n ) L _%_ &_-
uL Ln a) -Lt n 4-) 4.
a_ L- ( Ci H- Q 3:
CD W-U--- Ha) '- CE L n uC m -CO0
Ln =3>- a) (n .- ) a-C 0 ) (UC) E ) 4-'acn Ln - 4-4. 4-
-i >) -o C(A m-0 -
u c C CL. * 4- 4-- Q)4- Uw 0 u.&- u 4-UJ-> Z::- a-) 0 E cn 0.- 0
V) .. L C) = c Ln CO an>- c: ) ea 4J U wC-0 - M V) Ln
l :3X _c CE .- ' 0 Z I- ) 0Lan =D(3 __CD 0) d)Z-j
L )0 +C 4-QC) U.C U a
>,0 D.C 0O 0 ) d)V (VAH- (A C)C)-11Z-. L C
LC .- 4 - ,L a)C a) C a).C d4 ~0) 4 - I rod) Cl L Of E -EL
C.-4. I)C o v ~ . )- -L LO4. J(A f H ~ HL
- j L c~
a) LJ =: C. -C
C -' -5 m0 L-) C
4 V) ,I-O C. v. -. ( 4)4- 4i
C : UJ~ 4.:c 03 .
-4 (A
C:)
I -
V) -J
-j
co m
>- C.L( 4-
anj
cc 0)
-z 0
-:X - L
A-- Li.
a0 a) :3 U
CC 0CC) L L E
4-' 4-'
55
- 4-) 4->
-C) 00
CL 03 0: L
a,- Ln 0 feo toJ 4 '- (A .4-
U~ 0~ c~ (A 4-0-C1(n .- a, *- 0 C l
L) LC 0 0 -Qi A - 4 -- 0, C- 0
-~ 'a0 CI-,0 .
- E u _0 U 0-0Ln =3 ~>) WO) 4- aL,() 4--)4--)
UL 0 4-. 0 0 4- M4 QL- mc. z:2 ro - 0- 0ow
- 4- LLJO0 :- - 0-- -' oC C) E-cC.) *- 4-1 E C f CC 4-) V) Cr
=D ~La,0 -C cC <z c . <0 ca 0o30- ~ u C>U
( C) 0f -0C -F-- L- D allLE eLr o U) 4 --,
La, aL 03 o. o U , J- ) C 11cl.~~~a a) LU F ca
S- LL- ..- '- a, a)~- i a:~ 0a)4) ME Er (t = 4-) 4.- 0
LuJ 4-) F - F- ~ F- F-O 0 - Of<
LU
a u- C, C'C
C Li 4-) L 0 JC ~ Cof 4.) <. CL. *
C CLuJC~ 4-) L() L)
U - -
C)
Lu C:)c
- 0- C:)
- E-
LU 0
cc C
L Lo :3V) Q- U
-U (A) '
a, E ) -o
56 '
0 (1)W
0- 4- vECW43Q
0 .00 L. 0
LAJ () > C ev Z Cl-
C) - = Gi 4-) a)
110 u 10 L a : .C
z x uly Ly' Cif- P-EL)a
CD 0) ~ C 00C- -u U0)c :> E L c
V) 0 E00 L<
-j 4- 4- 0 ) 00)U~~:1C ~a 0)0- 0)0- 0
j:: CO E- CY E)V) 4~4 ~ - - 0 .- :: -
>- 00 0 c-c )0
w L L. 0 1 Ea Co a
cn EU EL L
Qy' 0) y (D~ 4-
L W <r -< 0 Cf<
V')
c'-J
0- LA- -i
>-L 0- CC - ' I- U
~E
4-
-J L
C-1 )
o
00
457
E
L n
a'C ~> 4--)tn S:CQ L-
a'.V) 4- 0.L L0O -0 _- 0) LI)
4J ) aL- (In m a: m~ c
a) C - c 0 m( (U 4-)i4 L- a'4iC F
u.) wT Wa0 F- 0 -- ) _043 C n C 0E Cj 00 0
LI) (/I v)a) tnCD 0~ > 0WC a Ln L- .- (A
L-) ca 0-. (0Ln co- W' (n :3 <c>)LL- J C 'a ( f-On 41 -0 0 0CTcj 4- V
-(0 0W a) 4- (V C- a' WL 0OWL. L Q m -)L -;- EW a)
C 0 ~ -I (A .- L- (0 " m(0 c Wa)- 0 cn a) _z -c - L E LLn - tn 0 uI- 4-) uW a) ( 0
co ' +-0 L 0 co0E 0CU aro OL- 4-, a' ua) LI)() L. 00u
L- 0 -c0 <WJ <ZW E(
(/A C: U *.)~ QQ (n a)I 0 ~ a'>- 0 OC u-C - - L- L- c
(0 > _c-- V) ( L. 0.- LEL) W V -ai .' =3 Wj (0 0 W
a' 4- L (DW --W 0 C1c .(4.- >,*- 0-)
u (C a) 4-- 4- 4)0 C c 0(V 4 -i to0) a' m (0 (a - aW4- Q)L- - aL W>1
eo c- -: ec 10 -N
- :F m0 ---- <0-
4-.) 0:f A V) m - 0. m
C .CD
CDcc o 4 -
>- zj 4- U--
Oj (o 0-c
: -a ) a'
F- ra' 00'
a) u 0
L, - i <r, U, .
0 00C~ 4.J(58
C. -C t-f _ V
4- o- 0 0 OJ
4) 4L. 4-i Cjt0 a
4.-> 0\ 4j -4-) ) C- 4-)(0 4C) 4-A Q-
U 4- 0 CV 0 0 0 u
tn -0 tn =3 -c*~ E LnC) n ) L n a-f L W 0 no1 ) =
4 - C\ - (n) 4- (A - V) ( On 4-
a) t/) 0 ) a C). 0 (1 -C
- 3 c 0a0) 0 a 0 03 00 0
L- EI I-A EA E, L- cE L- -
0-~ W(A fl. c 0) OW 0 .- 0 =3G 0)ea
uv 0 u 0 u~ 0 -
< .L E .0 E E C)> .-- EL)4-- 4-) fZ c = 4 r O3 MO C: o c (z 0
-- >LU C- =:t5 fn .- =
C- 00 00) 00 0) -
CL 0-CL E E 0- (- L- c
o. C)t L - ai L- a)j- 0 L C0- 0) (D 0 0 ) - - > 0)
I_- E_ c-r L L 0. L- LL 0)
LW ) F- LO . .. L- L0 4 -) C LL
C L a)>)~ ca) a)> a) >1 C - (0 a)L. C &.LJ< Jo Lu>QJ LLu Z~- Lu V)
0)
0 L') ,u z-) : Lu J 0 l C) > C
-- z CD ~-- 0 u
V : 0. In 0. en 0- 0~ 0.U J 2=4 j-) ucm LuJ <C C
LuJ
co CD
CP) C4
xL -i -
CZ)
C) CDi
0)
03 ) a)
0) (A
L 0u 0.
C: 0)
0
x 4--)
Q)C 0 0C E 0
- 0C-
59
U
UA .0 CnLn .0 LM
4- CL (A F-
(n 4-) W 0 >)(A >DL Cc F- --
(J (n I43 . c- L) F
(A 4) (A*.- 4-)W~L 4.CI 0-
L.. U M L J. Q 0
L- 0U. -L V(A 0 C) 0)-.E u -- Ln = - Ce() (AUm
Do-1 0 F- 0(AC CO (>. 0 0c U7 LU ( ~ (C (A
C/3~~~F 01j C(5 W.- OWW'- I
0 z- CU V) a a a'c E E EW a) -y EWa E 0- E
ai3 03 (A :3 u 0U :3 u :3 - :3 0- c- (O : >(0 '-0 CL - 0( - i , .
c/3 01- 0> CL 0 L- C0(A 0 :3
0.- -0 4-). C (l(AL A-) U C0 4-)(C0 ~~. CC C-,- .E*-- 03 c.
c c-A C :(
LL- -~ 0.J LA Lc,0. LA LnW .W'-3 C fL (a .- , W- V W-a)
0. 0. 0.0.L >, - - 0.CL 0.0 0 -. 0. (
WL - 0.r WL*- W.0 W-L. ~i C1 Lu C~ a) -- : L-
C )
O ( -:z .0
LU l': I u- 4-)
u
C)
F--
-' I
CDICco "-
(A(
Of j Z5 (A
<c 0 0
Lu EuV) 0 U0
X-
-1 (A( W(
Q~ :3(~ CE
0.
6o
7) LA ) -
00* (A- (A-t-.- -W - 0
o~ 0 L
4-) 4-- 0 ~ U
LA 4-) U iu (0 0..r- ea~ M~L) Lro U.- Q( a)a)- -
-0(0r 4- 4)(0 :3 co:3 uLJ -y U (0 ra U .( A Q
C.- At u u L.- w n L- M -
c co) C:C CD aj- 0)iC2 c-C LLU u A E E 4-
E~ ~c o EC EU L) A -
L. 0) -- (- - _::. L- --- w0 4t.- 4-'Cu 0 4- 0 4-
co)Z0( 0) ::o( > LLJ V) 44-Cr) 0 - EO - U C ' 0)
U) 00 10f .E (= 00 4
(AAG 0-0 C WU')E 00L . - C 0- c 0.
a) 00 WJ l 0 0
oC71 _0 U 0 E o')(- 0 u A-3 j U 4.)L- L L. c (
C - a) L CJ* W.CI- C - .
Cr)a) ) 4= - LJuC
-c LU CZ: CD- c.
4-) D V <c4~im- ~
c LuJ O -- o:: 4-)0 Cn Lu <c
Ul
uLJ c-J
jCr) I-co zz I-
0
V-)
C-L
0 4->
0 C-0) V) U
E on c C:
0 0.V(
4-' )
4--,~
8E C- c a0 00 0 0
61
4-) Z 0
LA . n aA ) (A4 Da) -- E u
>1u 0F 4-3 >1.
.O A 4-J L. a) 4- QC.) CAL CI -) L- V
) u r L u WL 0oUl - GI) C) o.' )
LU. roL tic$ c C - (a 'V--~ LQ. C U 4-)4 4-3 L-) 0)* ~ L
Z: > 0 eo 0. a)~0- -' EAEOA 0U
a) 0E =D 0 Ct) u- =A CU) 'Et Ci ) .-- cot7) EL
a) (C -c Ln 4-) LC:~- F- *. 0 'V 0 0 >,- F
V C= (AU 4- 4- U0.- i Qa >O Wt ai .t) (-n 0U
Ln 4EE CC U)- C: >.- L) ol D-0 EJ .- V) C- C- u0 U C- 0 4- =L u C.~ C 0.3 CL a) cc a)
L. =) 0- C ( U 4-)L. -L.4-) ZDc
(A - u.C C) u U C) = ~ C- . )(j-*- <U a)0 L- C -- C.. mO *
ai u~ L- V) cL (t)U 4-)F mC>0 CL I- CQ. C - . L 0 ) > LLJ 0D.C
L0 4-- CA U ) ~ LC U1LC 0 ) ( L (I L ( ) L. L-WI UL ?v CU04-91 4-)E 4->L 0 4-
cu * -.-. ) a)- LL 0C) (aL =3 0a
:c~ co . (AJ U)C W0. -.) L.C -'
V)V)
LLJ cl m (A
U) ) LU14 -J 4-j -C..0>c'I LL =. -, U IlU-
C: - - M: - C ct C-4
4 m LU J <c C.) 4-3-' ~
Uo - -
V)'
co E
E U
UF-U) 4-
Ln M L0- (10 >U
4.) to
Ct) 4.)
L )- 4
LU ~C60
McC
4-3 0-m :3 0
t 4 --)0 c- -3-
30 0 of " 0
0~~ ~ ~ W-a 2:CLU - 3:t) LL- c 4-
c L) . 0 a) 4- 4- (U-0)1 ,- a LL 0u 0 L.
< (A LLU QLI -0 uC-) 0 0 (c LL .Z Cv'
- L. ~ L u0 U 4-0 4--) mLL- = (n0 e.,- (AG 0) ) U
=3 eoL 0- C) L- a)
5 00 LE 4- M7O 0 U0- 0 0U (a ~ - 4(.U C. (U
J) (DJ (U d O
L L-0 tO (a. C. L0 C3 -M E
4-) 4- -- 0-0 4- Q 0 cL 0) D ~(-4 voW L.0 02 (1) >, -L C -
0-C-) C- E 0. - 0 0) a) Q
>- Co oL a) UA U0 EC CL CL Wc , = c>- ~ F-, (d. CL C 0) 0
m- >-W lio ~ 0je 0(d Q) 4- (dW- CL- L. I- ud( EL.
eo~0 >., - 4-3 a'. *-C)0 (00) C- (do fo J-) >, >~
C40 41- CO 4-- cc0 m) 00 m
(A Nnt . EL
cU 0 rc0 a U naLu 00 C- m d4aWJ o 4)4 F-
0) tf )U - N
LU F (D 4-3 ->. >-LUJ C4
*.- ~ 2f) 0) --. ULJ .4( JA C
C LJ ULCJ .0 c ~ -~ c 4-J
Uj C-'0 ta)U
V) C14 I
(A N .14
_ -
CDA
co 0) 0-- V
4 -I n4 -(U 4-,(C I
4-LM 4 4) C: 0-
czi =3 Eeco L) (A
U -'4- -
0) 0)
63
0
4-3 0 0 0-0
0 0 w 0
1)- 03) M
LUI (0 (o 4- ~ -4- L-
01 oC 0-0Ln (LW U), C CA C 0
4-- (A C (A -' 4'4 44- 4-) 4j- 0LL. -: ~00 'c-::C -
- ~LL ,'CD E un E 4-
V, L- - 0 4-) 4-)0 a) ) 4- 0)4) 4--
i 0) E :0) *,v *r.- 0 *- A - 0 .- )
C. -LL) 4--)4-) 0- 0r 0 - 0 0 0 - 0 4..- L 0c V.- cc~ (A cc~ 0A~ 4- (A /) L
0 c 0) 0n t n( n -Q- D L- ev =D 0-- - : C- :C0) <c~ _C:
=)A 0); -0 0.> 0 - m - Q - Cr
CDI -I I- LW 0I- C'0L' to 0 L
L L L. L- a C7 ci 4)-3 (D 0) 4-) a)0E:
0)J4-) 4-J ai)0) E co EWC E M E E ~ ELU 3:LU WI-- I- -LL- V- -C o -2
a) LnLUJ
- Li Z" LU I.
0- C2 0 4- C)(
V) 4-' 4- -l c
LUJ
CD)
Ct) I ~-ILL-J
CDCC a) cc.
0 lbCL C- C-OL
E L- CC -D.0 U-04~
C-) 04- c0 0
LUi L. 0) () 0 -Ji ro =0 u0) C0
cc - ) C- u(Ij - 0 -
n - 0 C-1
Ix L I4-C) C-
>UD ccj.. /
L) (L
a) a ) 4- 4-)4- - j4 : L-
0 U- 0 L- C:C-
a) 4- a u 4- 4-'V 4-j
4- CC- 4-~ a
mJ 4 U*- 4L ..- ) M LL- 4-( 4-
4-4- 4-) C L ) 4- 4-Ln m (
U-~a U-a a)UlE) c/ E
-) cu (D a) .0V (n = (a (A4-- *r - -- 1 L 4-) 0 4-) (A( (A.
-i M75 mm r 0 M- CI L0 0.<c - -o - 0 -J E cL-) a) a) a) aO ) 0 (
04 L - a ) r 4-)' 4-) 4- --V) (n c (AV n c v uV (VO MV (V CL
tn (A (4-) (A LO 0) (n~ = naC) CC- Ct'
00- U- a) iC- L a) C) C
U- u-C -O G QJ 4- U - a)u
L/U- (JO E. (JaL) LJ- L/) 01 4.)C-4- 4-C)
(A 4. ) ) Q)4 ) a)
E m E roa) ra )
a) C: c
*'- W0H .0J w CL
c - - i V) 0- -. u. .*-
C O f) < CD 0)V) C4 = )IU UJ 0 = ~ a 4.- 4-- 9- -' CLU -u J < 4- __v-
9- --
:)- '
-j C/)
-- 4- -Cr 4- a C
IL n
C (JO A I4--4-' 4-) =V M;
.0) L- 0
00 C'C:-
W-' CL L
CD0 LUC u rN
65
03 4--
4- U) ) 0 4-(A a) 01 "o 0 0
4-) C - 4- ) rO
a) 4-) 4-) I -U)J CU L., 4L (0 0) a)nLU-U a) a-)C a 4 -J( ) U)
-a - 0) 0. 0- (/- VO 4 ) U) 1ct~0. LU) a)a)a)2 c .
E) C -4-) CD w) 41-3
L- C 'Z- c(V 0 ~ )
- 0 04-o 04- >) La) ) U) 4-) a)- C-) a
- 4- 4-) (A)U 0u E u 4-'(1) 0 =3 C-~ (D- Ca).- 4- to
1J- L 0- L mUO - 5 0' a)0 LJc>- <~ ::. ) - C L 0
- a) U) >, 4-a) U4-3 - O 4-a L 4) 0 ) <a- EV EC CU)4- C) 4- E E
W- a) CU" MU) 0 ) .~- L ( LIa
Q) 4-~U a) ( - Ca) . 0
n aU) a1)-( a)) 0- L c - - V CU) 0 4-) MV, Wc U
-C C) >1 -C > -L- >, -1 oC'-P a L04L L0 L C -a) 0) = 0 = . 4)0
-' CC W CCJC U a) C i WU)- (aL 4-) cC0>,a) L Ca) cuc c 4-L. C a) s_ a) L
2 j CL WJ jLU LUC0CL uLJZ'. F- CL
4-) =>- C, LUJ C_ L
C - - 2 - 4- 4-
CD
C-,-
I- - -
C:)
C:: 4-)CC -k 4
V')
C7
4- 1 C
4-i 4C-(2 Wa) 4-
Lj fo CU04
a) U) L-
a)a4-- 4-)-LU m La) OJ
M) -C 0 -(L< Ca 4U -V)a
'7 U) - Cn U) UD
0 F- 4'
.- a) V..-66
4--) 4-3-V
4-' =34L- V ) CDE
V) LCL-
C15 0- -C Va) 4-) L
4- U- (
3 0)- CC C') a) o- (L)LU a ~ C0 ~ 4- 4-
(/) ( 4- c0(Dfl( .S (A ul :z L U) U- U J)
C-) VI :3 - -0 (n0 AI) > 4 - 3 <c 4) U)(
- Cl m' ro) 4- L 3430 ) 0 0( C- c a)< 0 <
-~ ~ ~ C CO) '00 ( A 000 0'CL ( (A4-'C 4'
4- 0(A (,1 ~ a 0 V '0. '0
C- a A a F- 0a -J Q -
- : = a) >-4- 0)0 m s _fALC (nA;'Ct *- 41U) 4- D ' 4- -' C 41 (A) (A)43
c' )c )V a) 0)CL . 0) uC <4-i
? 00 a)C Wa)0 a) 4O - - X
Ct) .- ) (AC4- 'C ()0 0
0) UCI 2:: 'U (A _4- 4--
Of(/ ::r( L-'4' A--) 17- -'a a)4--)A A0 4-'O-1C :4-
C (-L '- .- 00))aC 4 ,>
C-)
V) C LU
F-- LU I-I -
LC/ i C) x)C C- '
C)
'-4
LU Ur) C) 4
CO ~ -- tnCjJ-
0)0
0)4 3
CO 67
0I4-)0) 4-3
X (0
><0 4 ) 0 Ln 1-
L3U tA LL 0-V 4-) ULu 4- IVi.. 0 V4i U. )
LL.~Q cO U0)0 (AU-
U,~> (0 V0) 4
Cf) 4- >=*. u E>' E -0V-T -- -0E 0 to :3m =V
j a) m (o 0)Lc 0. Q.~ - ) 0 M0S4-) - C: a) J- (0 0 C.- .- 0)
- 0- 4- -V 4 .C- 04-)' L C0 G) - - 4-'. 4'0
> n U 0E C)- (0 .- -30. Q 0 UoC c 0- L- to E c (0 C:C)11 00 U0) L :::C C- :DV LC-L 0 C: 0C ) 0 a)0))
ra 4 ok-' 0L.- c _rIL L-0 Oa)( 4 - m- 0 (0 (D - L- 4
C). .- U- Cl VLU -u L- LU> (0 4, lU .1-'L, C W00
03)0() (00() 0)0 C: 4-' (0U , (n rnou ) ro 4-)0C.- 0).- c (V0 0 0) tn(10 a) C a) M0-
LLJ UJ Lu:i W>. C) I- 2'>*n
(m -j LLJ LL -)C4a) ujiF- _r_ -N,~ u
0-- 4- -lE
0 0 u
- w CJ 1IV) I
-4j
0. I
4L L
0))4-3-i
co Ai CD
OU 0
<c a) 0 U
4- C: (/ 0 4
a) ut
0) 0) -
68
44-
0 0
4-ut 4-) u 0
C0 a - U ) D E
0 4- 0) =E - a-oJ E 4-. 4- 0 ) 4- C:
V> 4- ) u - C ) 4a) m.. a) 0D >U ::Z
4J' L) -C --LC C C ea- a 4-) 4-') 4-') 4-
U)- 0 0 .
- E .4--' 3: '. ~c 4- a) 0
- (U 0 ) a)3 0 aV) E c E C )4--) 4-' 4- 0 Aj0
0J -..- 4-3 --to~ - 0 0 0 0 0 0 0 0L) > 4-') . 0- 00 0 -9- C
- 4-' L. EL U): cnl V)0 E M n 4-C) 4- , a-W ) (A Ln = U n U0
>- CL3,- V~ ) In~O '
a- -C 3 mC tu a) Wtoz (Ls ) 000, 3:U) 3:C -0 -I-
a) -a L C)- 0n 4- toC _r_ uo u U4-3 -Wrot C), toU 4-n. L,0 4- t
Q~.-E- ait MU U )- aU a) a)-4 C 4-)L- 00u 0) 4- 0) )- >.
10) 0 ' L /ru( n (v0 ( 4 ) 0 4 t4- Era E E Eto
V)t 0 0 ) ML t-- .- o a) .- 4- *4- .-
I-C CI-0 F--
a)L/)
C) .J LU 0c-0) j LU3H CD0_
> LU 0) CN C-)C .---': E -. 4-j : . -
I-. n :t V) CN 3 c't4-) LU3 : Or 4-'J-4 4-') 4-'
C)L
-' a
LU C) ". F
- 4-
-Jea C
4' C
-1 E4- ) 3
L L
4-.>
C: -Cr7 U)
LU~~0 CLon>-U
69 -. ~
4-'
( ) I d
-) -
-o) (a) - 0CE:a) 0LU (A4 Ln u
L) Q) V) 0 U-1 C31Ln =3 c )( L 0 L-
C.. VI V)i C =5 a
c <LL I- 4.- Ci 4-S 4-') V) 4- L- F 4-
Cl) *' a 4 ( La) 4-)j-~l Cu- *QI--C ~ ~E md C
LnU (AW 4 0.- QCLa >-, 4-)0 O C ) wE Cd ju >)~ 4-1 (Z~~c W) > - d a -0 _0 -0 0)
Q- 0C. 4-' MC F= LE WO u- I) 4-) L 0) Cu, 4-E 0
If) a) (U- Q- C C) LL. i- CCL uL C 00 0 0 D C) u 0
Cl LOi -LU-0- C 3 ~ca 3: UH
0- 0- .0U 4-C A.C 4j -Cd (- edo m ~ 0 - U- myV)
a) WE e'.. -e,0U LL L WD 0) 0 L 4-i _l a)vE a 4-' E -)L- a) (dU A -iLn 4- oCC eo Ul e C c 4-- a)- a) ru J_~C L 0 L- CD 0I- 1±0 F -C~-
It)
_j- LUQ) L U - 0 IC--
=3 :> C- LC) CD u- x U
41- L U ' ;r- = 4 4-3 4-3 > 4 - i
CU C0 -
+ CL. KLU n
C- 00 0
Q) Cd t
0--
E Wd
(A 0d L0a)aC- (/ ) aC
I 4-~ (70
4- 4- :10 :
W 0 .- 0-0 4'o L- Ia,
LU 0-4-) 0. 0 L- E .(A) U0 -iE owQc E CL- 0
4- 04~ 04) ulc (n --
- &~a, U~L 1- 4- -
(n 0) V~) L 4- _0(D a 4~)LU 0LJ 4- I 4-- ~ , r ~ a, a, -, - 4-)
- ) (n f- t-E;tn C 4-) u U)o. 0 a) co3 (a0 (0 OW(
-z 0 QLC/ (AW _r_, a). (n L
- 0 ~ < a0 U 4-0' L0 CL E 44 . C
(0 0 .- -E C0 a-. .- ) (aL
0) L L- aj >, V()L4) ai 4- 4 ~ CU 0-L 4-)a, .4- ro0)~U eo~u cm( V)m 0 -C 04-
E 4-- ( := ~al C4jUCY)c a 0 - c 0 w: 4-a)0 0) 0(0
L ( 4-) 3L4- 4- L 0 4) 430cI a, aWL (a.C -r ( c-_LI roL C a 0 WL C
V~)_ U0 24u 0
0 c
L
LUy 0
T, 4
(I) (
0 0
c
LU C44-) 4- 0)
.0 E ,.-a-E .- 0ui
a, - L-
a)~ 4-- >('- a7
< 0 -~*~ 4-'- 40
71,
,- C: 4-' c -
0 0 -u A-) 4-' W1 raLLU 0- L) 0 raM
C) 0 f 3) V .- C
x 0 a 4- Ln 4-) En' D 3:-a) c :c W - 'A-
S -) '4- EA- A 4
e. a 0 10 Lm
Cf) = = -0 C7 *. L--c 0 0 L. 0') C- u' U)
__-j a) c c- (a C-) 0 W ( COWc) 0a 0 cA' 0 t V V
C) CC) ) .- L C 4- 4-) '4- V)' Ln ) VL- a0 *.Z a) Co- 0 <
V) aiC '-- (v4-) (3W u c ucn 0) L. L . = 'A- a) 0 j3 0 0W
SE :3< 0 - - I - - C
ai c (n W'>, Wa. - _0 u u QoQa -L0. - 0- ra V) a)I W L)C
L-H C0 - O i V I
0) 0 0) E - 4-'A 'A 4- U)C.. r ~ L E LC L- m 'A c V
cLI. E: LU0. C UJI L- 3 . I C
(3- DU 4-- Q)43 ( Q : M
C)j .- J LUJ C-) -
W u =UF- u:CD LU ca. C) > ><
T;- LUz 4-3
C'-
LU C>o - m > X
I4- Lo -
V) ac m.0to 0
>1i
'A 0
Wcl c.. L
LU 72
C:C( ~ 4- Ic u m~
o *-'- 4-
L- 41 CD'
C.) . wn -Ev)4 - 4.. 4 414-C 4-) 3:C.
LL. :z 0 'v -. Ce
E~ 0 E) 4-- I o 4
=. j.- :3 0 )0 () 'v w. 0 wV) ( 4-> 4-3 4-' 4u. C:
4- Li. 0: E ~1 c )V n4 WO () c) (3)
=-4 C*- (3) W v O(A) 04- C- 4--4' I oc-
0L O.(n U.) 0~U 0 (OU L.ai ) a CL -~ -v -- 0n ~ u <
CL *.- 0D ro' M) 4-) .00 .C. 4-- 4-)' (4-- 0n >1U C
- > .- U)n (~. C WC(.1 C C) E) 41)0 a) ~ 0~
L. 0C C-- c 0- 4-a) -) c-C E1. 4- 0 LO - 0
OL C 4- 1)
V) 4-)-'C
C-.Ci C C ) CU )(1) -' =w C -C cv rJ, C 4--
LI)LOf L/) <c m.0 -
4-) LL = = k1-4- 0 .0 0C: Q LU -se c. - . '
('4 0' .4) .
CL C)LU I . ~ 3 ~oL - (
LI) c(N
4- a)
0 0
C)
-LJ I~-C 07
0 0UL
C)r 0r
C- 4-
E 4--)
0 0
~ 0
(C 4- 0 C
Lu4- 0-) E
C)E c E 0CL711 U0 C 3 u Q)
<ct-L-) L- CL 0-L-) coCC a
4-) 0 0 0ca (U-( m ~ 4- 4-) -L. W
- 0 4--0
CD(A 0 V) C a) W C
Cl)i L- rC 4--) Lof 0)o - .0U -0 c- -
0- E E (U 0 w-~0 (A CDU Q a) .
C-- C 4-) Wcn -1- 0C 4- 0 4- C)0 cn
a) 4--) 0'- 0 cL- LmA OW OW
:3 D( o- OL 0 u -' -CO
0-T a-(-) C c >-, J-) >,L-(J Q M 4-' (C 4-) . 4-. 0
Ol( Ln r4--) 41 c 4j -C -EmC m (AW Q) Cn C a
a)- 0 0 ) Z3 a 4-0 CD 4-4-
U) C.- - O cC
(4-J
-C _j wC C-
2:7 CL C- > C)
4-' WLLJ 4a) ul
co ) cN C'N
w~ I rI
X N (N
CD
V) H>4A (J;(C
I 4-)- -
W C-
0 4- o 4-')-- - Q
0- u ~ CL (A -
4-4- V) -)
74
4-J4-
CL
c 0) I- M CD (-> VI LnI(~:
(A 4-) ~4 4' 4-) -
~ '~ 4- 3.1~- 4--) 4-.) 7-t-C--1~~r
CL to 0) ) 0 0 4- 00 4--C) 4( 4-)- -'O : x 0- C
(A0 CA-' (aZ (L -c:-C (A a)C (A u u
>- l 0- 0- 0. 0 C <C-1-- 0 -_c- > ._I- 0n = En C) (A )
UC .Z 0A (Ac 0), <:--- < 0
04- 0' 0. 0E
V) C)- 0)
-zrL 420 ro( Erv E-L
:3- >,- _3 (n c nL - L r
40) 0JI C) 0 a)E E
m- - c c)-
-i I-
LnL
:3 21 W 432 -
CD
F-l C.-
CDd
C: 0 12Or- ) (A70
.J (.)C- LO C
cc C':3 4--)
M. - -0 d0 4
C 04--C C<C$0 LCx L- 0)
L: 00 ) (A
C4-ut (nO
4-) 0
75
4- 000
C 4-' A(o ~ ~ r Q)(1U )0
f0 3: ix0 x
4- 01) 0 40) CL0
C)J 4-n0 LL ( - . L L
(A ( LLU 0 0) 4-- , 04C)~ - 0A (c 0 E u
L Lo 0 U ftL- (/ I-nUOt 4 - 0I) CL
- 0) 0)~~~- )4- LE 4 L.
a)/ ro u- =3f U o mf-a0 t CD 0C : (A 4-'0) 4-') O
.- J a,- m )r rt w) M< U Uro 4-') ::- C- L- L-
) 0- 0 . LU 0) 0 a). =5 ai.- n LoQ (A f0 4-'E (4.-- Q4-) 4-) CD-4-'
L/) (A (A4 M. 4- LL 0 E.- t E-Ofr J_- (DC 0 I )
0 ~ ~ ~ ( FI ) t/ A- LC.
L t.- f I- t>~ 4--) U4-) 0) U 1
V) M4- >) L. ft Cr. - W .X C 0 0 LU L L
4-) a) I L ~0 .00 4-) 0
Er- ft 4(LC 4(
03) *.--0 Z).- 0) u)A C 0
0) I F U
4--; LJ Of - 4-) kD
C: <__414-
LUj
I -j
-j
.0-C4-'
C-)
4-' C-) U
LUJ C Cf ft ru-J 0 0-
-n 14-4- 40
n) (A:30
(A ) C) UAL )C)-A ) ftt0)-0
cn c 7 4--) 4.0-3
LfE L Eu E
76
a)
- 0 C. 34-
nV CL 4 - (V
4- a)
-i LO V L L
2: rV a)) a)4- a) 4 0) M- ~ 4-)
c- CO -V m) a)nWj -C eC I- 2-C (Vto Ln
2 . a)I 4- 4- 4- a)a) 0 L- L -L
-3 4- 4- V)) cn (.(1o u (aV a) a)V
a) (A = X c -C&-
~1 a) (I2: a) C2 U 7 c
- 4-) 4- Ei( E( 4-- c M
--3a 0) LL t- D -
8I Laa 2t. J- CL) UC
=5 Z::) CC uj 0
Of LU
c L- 4-18 4 j (c2
L')
<a) t±J
CU r .-~2 u
(I- UU V
0-
L:r 4- 10 C
4-- Q)4L- 0 C
U U-Ea I 3)o
LU ) m'CVuC
.J >7
L E
(A 4- 0 4
> a) 0 ( ( (4-aCD E 0 u) 0 >-) -,. (n
D: ~ 0 E --0 ( 0 LOc0 r >.C (A C0a ( 44-) E) L-Ln0 C0 ('0
WA a)v COr .-Leo 0- <*' - -00 LL .C) 4JV 4-j 4--E I4-' a) - 1 F- 4-'
~~~~~4 *rE VV 4'
U (nC (AV)a) L- =D c 4- VI ( C- n :> n- - () 0) c-V 0(A 4->'
CD. 4'-' 0) =.-M' mC 4) 'o ~ tf- L0 W) 0 L(A 4- C:
- )- aa) (C u0( c-E ZD a F-( vCV 0 aC- E EQ. a n L- Z3 ) 0
L'D.- eo C a) LcA a L) C4-' £' (-- ) ,-L. c:>I- Q C. WV) a) 0 OV( V~) Q
0 00 00f- L- 0.*- LL- La) < )C . a) 4- F- L.c a_ I:c '10-
- 44)C >), >. QV)C-f) Ei'4 =)C eo.- --. u7L 4 0 L a0
u C: 0 7 CC a)- E (10 <
eoa) (D m 4-' LuO U La) a)I a) CL4- I- -- c -u ~ tLO t- L> =3- U0Lo ). aC ) CV i WO 0C u o aW0 (J). CC)O- /) 0C ) >) .- 0) CL -0 *- :- C-0 Cv a)4--
4~ L- 0 Ln. 4-' 4 E. L.L
m 4-'E mV a) L ro to CO 4-) ra a) 4-) M 4-CM
C-)
-C CD -i .0Ja) U - - 0- CN0 >C' 4-) C-) 0 -
4-- = I 4-1 4-) 4--
W -4-3
CL
II C)i-I.
C\J ' C\;i
a)
LL
<r 4. C 4-) 0), , C- ::0 0) 4-) L
0r a;CLu a<c -U L - A , 4
vi (/) m C-.)L
<~~4- 0-C V- )- c 0 eo a )Lu
>.F CC-( )C
a).-- V -78
aC)
V) c a)
LJ'- (31 (3
F - -- C) (V - F0 c- C)
3) U ~ CD 4) = i-
LU (n C C) V) (VO n cC) I ec L 4- H- ~~~4 (te- ( O
C) 00 -0 Ia) 0A (
4- Q)-WL O
>2) 4-3 ..-
L-- m0 LE~
'1 00 0'- a) -' 0
- Z)4- = (V *(0
(I . -- 4-' L)> - X . (
> L *rL/) * C 0 C) - Ci
C O 4-- * a 4-(
C- )C ) CC .0 CC C
W-0 W ua)
OC) O.( E C)> .
> 00-C)-0 4 O -. 4->
I,)
V,)
(V- Ic.
-C ) LU C COfC
a) LU I- I0 -0Cell
C >0)LU F .........~
oc
-~ 4-'
c~ D
o 0 W
4-'m0V 0
L- 0) J)CC
V) Q- 1) -
0 -0) (3) L4-(
(<) Cl 4-'(A ( 014-() 4-(V3 - L A
uV. U1 fu (0 a)o(C- 4- 0)
~ 0 (A1(V(A 0- ~Q- C CD C V)
(/C E E) (o ) -
a) a) L. -r -ZL- L - 0 0
(V. -4- 4--'
4-) ( 4-3 ( (v u .--
cu ccW(ia -- 0) 0
4-- 4-) (0 4-3
u. 4LJ C 0)C0 C
O)(V 2f, >, Wca.)
La) L/ :cH H---L.
44-'
CD
o C) (A
C) .
u QL CC C
<3: ru C.)
CC)
C- c c
C)80
(A C
ai Lni3 (
EC)4- 4-) C
C3) a) (A
C)~~ 0-C )C
CL E C t
CCj - C) L
L) ) E L- l) n )(D 0). 0-L4- E L G) 04- -:C ()
< EC ~ U) C) ) - (n 0) V-a c' CC 10 tC: E "(a V
L- L-C Cto L) Q-U Uo :
= *< H- C r o - C -02 4-J 41 > C 2
02 cv 4--)*- -to 4- Q)
- =t +jt CI- 4-) c
VJ) C-- CC 431 a-) 0- C
.J 00)VC C) C) C- -- 041S 0> UE4) 4- z 4-, U -)C
a.) c (0J to t --
c (A (A 4-CE ~ 4- 0)) (C (AC )) )-
C cC0i cc < I 0- a)Ut
4-( T-1 C) I > 4-( 4-) 4-4-
0 ~ ~ (DC UJ cY c. a)V X a
_0 W0JcrC) C JLJ -T0- 0-
:2 J W2H -C U U I mC : >C:)w (\J C-) L)
- - M C) -- u. L-~4--) i C L -:: C-) inUf - . C-) cc LL 2 *>a 4-' 4-') 'o - 4-)
C)
LUJ
CD
x -JJ
V)
C-)-)
CLI 4
L- erL
rto
C: C)Uu U
m. :, 7CL C- L;(
- l 0- L t
CL C
4- C:2 81
_0 _0
CC0 0
- CC)c co0
LjJ C- .0Cu kA -Cu V(( ( ) O1 a0) cu () Ln V)S4- :3 Du' (n0)
CA j Oun 0u C ' 0) vi- U CU , S- , 0 00)
m L- c) L- 0 a)-
4-' 0) U)0)0
- r 4-C- 4- 4- U 4- 4-U 0QA ) u'0 tA u- u'*.- 0 L-
c c CE : CE 0)(Um f era .- C) 4.-
CC - C- -- L. £c C- -C LL- Eu')u -E F- F-> F- =-)C,
- C U ro C- - rf(AI C- 4- C 4-1 0-' 0- -10 ( 0 L->- ai fo> 'UE to0 vu c E .-
Cl- C: 00C 0) -- 0 )-a)4-E _I_ _c_ -
4- 4-C-- 4-F- 4-4- 4- G) C Go 00) 0 U 0 00 0 U C)
0) a)i 0 0)))> 0)0) C- 0).4--) .41 4-)C 4- .C 4-' C 4-. - 4-4-'MU (a o 0 M (4-) fuD 0 cc4-) C ) W-
Of C-- -0 CC, L.) of > a CD :3
V)(A)1
- 0 AL l nU
c) C.. LJ C u.- 2 :A 0 - -r C D U 0-.
4-) Ln < C-) C-) C- C)- 4'
o CcoJ ( 4-') 0oU _ 4-3 1 4-)
CD
CC.m
F/- F-
CD
C)DC-1C CD
(A
CT
00
U- U0.
CCC 2(3) C-
,92U
20, E I-
tn*) H L- L I(U 4-' vw a) H-
4-'U L > 4-)
(CL. > ZD 4-' WL- DC CD oi u 0>4-) L-C L- D WCD
LUJ X L C , ) U~ L3 CC-) LJ (V0 cu 0.C 0Z: 0.)- Ev 20~V 4) (D 0- ~ - w L
W C: (0 L. 0)-*U Cr Lo t- =c I M CQ CC
Li- I (0 o L 0) 4-)r0 C-D - -- 0. r (L -z: 4() cC, 2 L- 4( -. "
CD .1 -' ) 0) 0 04-C '.Co C-I 0 4- L. U)
0 ) C m-2 QLn WCta
4-) (U( (n- >4 0) WC7
- --~- C0>C >L
>- <rW > CC 4-) vi tn W> c vi CL-
Cr0- Wy a)C 0i(Wc CD- 0) CL 4)0 )
a,0 C C) 0 ) a) .
t4- l 10 e
LULn
w) U ~ -- 4--) 4j)4-
C :- 7 C) C) -I --C m" -c ~ 1 CD - wi C Ci 0 co
Of) VU2: co~ -C CD4 - CL~
C CL U< Z-' In - o 0- CL' U
LU CD- F- C)C) '
CC~~ in_ -H-H
CD
CD:
(LA
CL Ln
-i eu 4- V,o o
0~ Cia
C'\)CYC
CD0
C - 0 c4)c
44-) O0LUJCO-
LUJ >, WWL ( C (A- V) a 4-) 4-' 1
(o~ Lic
L) C>Ut5 4- 4-a
4-) =3(A (0 V)- 0 0 ~VL) 4-C3e X~ -J GI 4-- V
(V LL~ r) n- n 4V) )
4-ja W-C:( 4- ) o)
- . 4-3 (3) C <cV 0
_,e- L- 4- 4- C4--0 L4 : ai -) LA -n
(3) .- -cC (A . C.L
0 - ZO4- - C roc 0 ea W
a i- L- C. f -( ( ( 3 ) (a: ~ ~ ~ ~ L ai*- 0)- >, C
C((A I - U W 4- F- LW LU
to ( (C
C.(0 0 4-u ra > W- 4-W W--0
(n(-4)V4c-Mc)e
V) 0 LU1
WA F-:I LU) '- 'koC.J en0.- II ~
C)) LU J a:o j C) C)CQ CLLU C. c
0 :-: l 4-' -
LU a)
C: c- -
-j 0 4-j
.- LU c~ LU
C(A u (oCI CC C -)4
4- >-
m I4 _.- 3)-3
VU CC C.-
4 OL 4-e
CL x4 - a4) ae) a
I ' I , )
84
o- 4J 0 A
o 0.
-0 k0 -''4- (/I 0 - CL0 V
(n Co .i -u C
01 E ~LUC~ L- =0U 0C- 0
C-) 0l C-I- 0
cr0
ru"-(0
V) 4-n -4'-' 4) 1C: -- (. 7- C1
C) C 0 C 4~ 0 C; a)
cu 0 01- 0- --V) 0- OfU > CL- 0) 0
o )L.-C -A '010)L 0 4-- 0)01
m1 01 L.) a)L CIL(ccO C) 0 ( 01 0) -0)-'-
COJ Of E C
-CQ CDL 010 (0J -C'-
C- E-4 cn- u
- Z f -4-J w f -)A-
0U0
co ". .
Ctf C C') C
4--) e'J
cc -J
C- 1 )
LU) (A .
Co C) L
-c W1 0
0~ (A - C4
' ~ ~ c (0c
>r r- ( a
(A (A 85
TABLE 2
DERIVED FUNDAMENTAL SCALES ASSOCIATED WITH ELECTROTHERMODYNAMIC EFFECTS
DIMENSION SCALE VALUE([17])
Mass M C 4.35 Kilograms
Cp
Length L kt 2.75 Millimeters
h
Time T Ch 4.16 Months
kt2
Temperature 0 kt6 1.04 x 10- 22 0C,or Nearly OCC2cpi, q
Charge q CF 4.2 x 13' Coulombs
p
86
TABLE 3
OTHER DERIVED SCALES ASSOCIATED WITH ELECTROTHERMODYNAMIC EFFECTS
KINEMATIC QUANTITIES
Displacement (L): kt/h
Velocity (L/T): kt3/Ch2
Acceleration (L/T2 ): kt5/C2h3
KINETIC QUANTITIES
Angular Momentum (r x mv) kt4/cph3
Angular Impulse (r x FT)j
Force (F): kt5/Ccph 3
Moment (r x F): kt6/Ccph4
Momentum (Mv) kt3cph 2
Impulse (FT) I
Power (FL/T): kt8/C2cphS
Pressure or Stress (F/L2 ): kt3/Ccph
Work (FL) 1 ktG/Ccph 4
Energy (FL)J
THERMAL OR THERMODYNAMIC QUANTITIES
Heat Capacity (FL/e): kt6/Ccph 4
Temperature (6): kt6/C2cph4
TRANSPORT QUANTITIES
Diffusion (L2 /T): kt"/Ch3
Volumetric Flow Rate (L3/T): kt5/Ch4
87
C)
-4-)
71U
4-) C~o0
(A (A4~(
L- C)~ Z3
4-) uL./') vi Cl
0 0A
U -
(A CL 0 C
(A c JO LLJ LU- L
4-) U() ) 44.)LfO LL) U- L - L L- )
ai (1:3 to C: () aia) (1)>-J (3) (1- -C - -
C))
-J4-
CL ~ 0.) 4--C0 > '. > U 0
Li. .0 . 4-4-
>). E
4- L
0t0.)
4-' 4Q. C4-' mL) 4
L- E. *-C
L3 EI C 0 c
a)2- C. eaC ( ) -EO mE *- L- L L- 0 a
E~ a ) 0 )EE a 4-L: M .0 (o
- L- L 0 0) 0)
co U L L .,- CD-
U 03 - 0 U 0 (3) 0) C
cc CO .'C C) LU LUi LL- LL ( D l
88
U)
C:c a)w ()c: u
Qc E-) (1 aU() a) .0
4-34-J co ea 0>ea ma -V -j -
co (V a-(1) C. a) - i
0 a) 0a LoC U UU tA
"0~ LL LL c-0.
C e (aa
0 E 4- -i-0L. L. LU 4
a-)C:
U
CL -P 4-) I ~ Iac() -.11 - 4-
C<4- U - 4) >- CL tv >
(a~~ 3- 4-0-( a 0
L L U - U > -- uI- -4- '- ) 4- 0.. 4- (au
CL > CILa > aL
0
(a (a 4-1] L) 4-
4-).,
(a4- a) LA3)CQ) V ) a ) C
L 0) 0- it II4-
4-D V) 0 LL *- aX- ) ai U -C, a)W
L '- - . a) .0 0 E -0 .a) CE .0 E .- El
.LAIt =3 E a)
(a m : a)C LA : 0a- 71,d 4. - ~ 4- - C
LA ~0 "- a))
0 LA 0 ~ LA U ea ma > 0S- m M: :3 a L- C- a) u
cc V . . . ~ ) Ln/
it I
(A 4-)0
89
U 4)
00
(1)3
C13 0
If 4-)
> (3)
a )j 4 --
C.~CL
4-)
V) 4-'
oo 0 _
E
CL
4-) a)
0 90
LUJ
af
LUJ
-zJ
- CQ-(t) LU W2:-LUJ
CD i CD
CD CL 0)0
CD >-cD -cj
M: CD2::3 :3:
-j -
co Of
2::
CD
LIJ
0 C0
C 2:CD 0 c
V) LU Cn 0
2: C) -- V
LU 0 CL
L'- aD V) 4-.-'4'
- -C c ~- ~4-) LiV Ln-
CD c ) -
0 E
LU~C aDC i e Z.3 D
~- 91
W ~ C~jE C
LCU CD -
LUJ
LLuJ
LCL
cvi
C-,Um- -- C
> F-
m
C))
CD 4' 4- 4-
F- C C/)4-'0
C:. 4--) '4-Q
0I 0
(D C
E
o. CoF c "
4-' 0 CU
U- L-) L-
C C E4) a)-
C cNJ 4-~ 4- 92
LI-LUJ
C:>- LAJ
LLLI
L(33 U
aI ca -C ca
<LU 4-) W
co 4- ) 4-) >
a))
Or LI.f
LU <
fr- u\ 7;I- E -, l
4-) U 4-
E >- to
CD C
0) 9-
LLJ
CD 0D
C-)D
4-3
0 iv
4-'-
0 Ln
CC- ev
cxn
<~ ~ 4- -
oA a a) M
F- cy
4-94
LUJ
Lai
F- -4 CO
LnL/ 4- I ~ 4- f
c -
a) -
=3LU
-j3
on Lf
~ 4-)
iIF- m- 0
oU 0
4-) C)
4-o
-1 0
c C:C -CU *.- 3:0 nLA
Of C) CL C) CL to Lie
oo U 0
4eo 4j 0o4.
C) 4-4 V) a) C-)
w- 10 0 0CD M) U U )C
C C 95
LU
Hl-LU W
af (X
wL C -
L i
.::c -le. -
LUn
4-'41
CCA
ea I -' -
C - C V
M7 mLL 0
-C 0A0
EE
UIA 4-'C)L V) 0
'V IA96
LLU
LLU
c> m
CD w a_
W W
LOU
-4J
C~4-' i
U -3
LUJ
co --
4J-L
c.'J 4-
970
4-I V) 4
4'~~~ -. - C l
U0,
F- C', LA- u
zb
C-) uC-4-' I- - -" 0
CL CLu~ U
CC 1/) 4-' \l
S - ~ -L.C4-
00
(NJ u -
4- c )r
-j e
4-'4 -
CCC, ) C C\J C V
LM 0*1j L- m4- a C
a) L- I-w -
C) C (N4-10V
C C*-98
TABLE 6
LIST OF VARIABLES WHICH ARE ALREADY
DIMENSIONLESS BY DEFINITION
DIMENSIONLESS VARIABLE SYMBOL
Blood
Arrangement Factor
Dielectric Constant for Blood
Emissivity of Blood e
Hematocrit (%) H
Non-Newtonian Index n
Percent 02 Saturation (Hemoglobin) % 02
pH pH
Species - Specific Constants for RheologicEquation for Blood C1 , C2 , C3, C4
Specific Heat Ratio for Blood y
Heart
Efficiency of Cardiac Cycle (Overall) nt
Efficiency of Cardiac Muscle Contraction nm
Efficiency of Energy Conversion from StrokePower to Fluid Kinetic Energy nk
Efficiency of Energy Conversion into Stroke Volume ns
99
TABLE 6 (continued)
DIMENSIONLESS VARIABLE SYMBOL
Efficiency of the Heart nh
"Other" Efficiencies in Cardiac Cycle nn
Frequency Component of ECG Spectrum ni
Korotkoff Heart Sounds (db)1 , (db)2 , (db) 3
(db)4
"Other" Heart Sounds (db)i
Phase Lead Angle for Oscillating Blood Flow f
Magnitude of f I f
Probability Density Function p(X)
Probability Distribution Function P(X)
Probability Range Function f p(X)dX
Vascular System
Amplitude Magnification Factor (for cyclicloading of vascular wall) Q
Branching Angles of Vascular Geometry 0
Coefficient of Friction (Wall Pore and Pore Fluid) sf
Coefficient of Friction (Pore Fluid and Solute) Sp
Coefficient of Friction (Wall Pore and Solute) ss
Constant Strain in Vascular Wall co
Dielectric Constant for Vascular Wall K*
Elastic After-Effect (Strain) E*(t)
Emissivity of Vascular Wall Ew
Form Factor m
100
TABLE 6 (continued)
DIMENSIONLESS VARIABLE SYMBOL
Fraction of Vascular Area Available for HeatTransfer to Body Core Ac
Fraction of Vascular Area Available for Heat
Transfer to Environment (near skin surface) Ae
Friction Factor fR
Generalized Poisson Ratios for Vascular 0iSmooth Muscle i = 0, 1, N
Maximum Strain in Vascular Wall Emax
Minimum Strain in Vascular Wall Emin
Number of Anastomoses Open at any Time N2
Number of Collateral Pathways at any Time N3
Number of Patent Blood Vessels at any Time NI
Number of Pores/Membrane Area c
Percent by Weight:
Collagen Wc
Elast:., We
Smooth Muscle Tissue Ws
Phase Angle for Viscoelastic Blood Vessel Wall w
Magnitude of w I wl
Pore - Free Surface Area (% of Av) Ao
Porous Surface Area (% of Av) Ap
Reflection Coefficient (Staverman Factor) b
Roughness Factor /D
101
TABLE 6 (continued)
DIMENSIONLESS VARIABLE SYMBOL
Specific Heat Ratio at Vascular Wall y*
i = O,1, N
Stimulation Coefficients for Vascular Smooth Muscle qi
Time-Dependent Strain in Vascular Wall &(t)
Tortuosity Factor for Pores 6*
Total Number of Cycles (required for hysteresisto reach steady-state) M
Vascular Smooth Muscle Strain &m( m
Cm 3,
Volume Fraction of Water in Pores p
Miscellaneous
"Activity Factor"
Ambient Humidity Ratio (%) HR
Degree of Nonlinearity for any Model N
Dissociation Constant for Electrolytes Di
e = 2.718 e
Ionic Valence of Species S Z
Partition Coefficient Y)
Pi - 3.14159 (circumference/diameter)
Respiration Quotient RQ
Solubility /1'
Solubility Coefficient
102
TABLE 7
OTHER VARIABLES THAT CAN BE ASSOCIATED WITH CARDIOVASCULAR
FUNCTION AND THERMOREGULATION
Characteristics of Individual
Age Yr
Anthropometric Build
Height Ht
Muscle Mass
Physical Condition
Cardiovascular System
Central/Sympathetic Nervous System
Endocrine System
Musculoskeletal System (exercise)
Weight Wt
Climate
Season of the Year (Fall, Winter, Spring, Summer)
Relative Humidity
Amount of Daylight
Presence or Absence of Wind (Wind Velocity) U
Ambient Temperature TA
Time of Exposure te
Clothinq
Amount
103
TABLE 7 (continued)
Type
Thermal Properties
Concentration and Properties of Carrier Molecules in Blood
Affinity for Substrate (Stereospecificity)
Deformability
Degree of Hydration
Degree of Saturation
Geometry (Stereochemistry)
Mobility
Diet of Individual
Chemical Composition of Blood
Alcohol Consumption
Quantity and Type of Food Intake (especially fats andcarbohydrates)
History
Family History
Predilection to Cold Stress
Frequency of Previous Exposure
Time Between Exposures
Myocardial Muscle
"Contractility"
104
TABLE 7 (continued)
Statistical Parameters
General Wave Shape of ECG
Kurtosis (Flatness Factor)
Skewness
Width Factor
Vascular System
Cold Induced Vaso-Dilatation CIVD
Geometry of Vascular Wall
Branches/Bifurcations
Convergence/Divergence
Curvature
FPrallelism/Taper
Geometry of Vascular Smooth Muscle
Length of Blood Vessels
Development of Flow (inlet length)
Effective Length of Pressure Drop
End Effects
Pulse Wave Reflection
Orientation and Distribution of Blood Vessels
Arterio-Venous Anastomoses AVAs
Pores
Cross Sectional Area
Cross Sectional Contour
Degree of Patency
105
TABLE 7 (continued)
Length
Mean Diameter
Number
Properties of Material Within Pore
Smoothness
Spatial Orientation
Symmetry
Wall Configuration
Symmetry of Vascular Cross Section
Vasoconstriction
Arteries
Capillaries
Veins
Vascular Lumen Patency
Degree of Extravascular Compression
Degree of Internal Occlusion
Level of Smooth Muscle Tone
Vascular Tone
Venous Shunt Response VSR
Atrio-Ventricular Countercurrent Heat Exchange(see N1 , N2 , N3 )
106
TABLE 8
ENZYMES
Dehydrogenases:
glucose-6-ca-hydroxybutynic dehydrogenase HBD
glutami c dehydrogenase GDH
isocitnic dehydrogenase I CD
lactic dehydrogenase LOH
maleic dehydrogenase MDH
Transaminases:
glutamic oxaloacetic transaminase GOT (SGOT)*
glutamic pyruvic transaminase SGPT**S=serum)
acid phosphatase
aldolase
alkaline phosphatase
amino peptidase
amyl ase
arachidonic acid (test for presence of enzymes)
aromatic L-amino acid decarhoxylase
chol inesterase
creatinine phosphokinase CPK (-MM, -MB, -BB)
dopami ne-beta-hydroxyl ase
gu anas e
kinase I
kinase 11 (precursor- kininogen)
107
TABLE 8 (continued)
k ini nase
1lipase LPP
oi-nithine carbamyl transferase OCT
phenyl ethanol ami ne-N-methyl transferase
prostacyci in
reni n
tyrosine hydroxylase
108
TABLE 9
HORMONES
Catecholamines (Blood and Vascular Smooth Muscle Tissue):
epinephrine (adrenalin)
norepinephrine (noradrenalin) (precursor- dopamine)
local myocardial catecholamines
Steroids:
aldosterone
corticosterones "A", "B", or "S"
cortisone
deoxycorticosterone
hydroxycortisone (cortisol)
acetylcholine Ach
adrenocorticotropic hormone ACTH
angiotensin I and II
antidiuretic hormone (vasopressin) ADH
calcitonin
central nervous system chemical releasing factors
corticotrophin releasing factor CRF
dopa
glucagon
growth hormone release inhibiting hormone (somatostatin) GHRIH
growth hormone releasing factor GHRF
histamine
109
TABLE 9 (continued)
insulin
kinins:
bradyki ni n
kallikrein
kallidin (lysin bradykinin)
parathormone
prostaglIand ins D2, E2, F2
serotonin
somatotrophin (growth hormone) GH
thyrocal citonin
thyrotrophi n TSH
thyrotrophin releasing hormone TR H
thyroxi n
tri iodothyronine
110
TABLE 10
NUTRIENTS
water H20
Amino Acids:
tyrosine
tryptophan
Proteins:
total protein concentration [P]
albumins [A]
total protein minus albumin [TPMA]
fibrinogen [F]
globulins: [G]
a ceruloplasmin (al, a2 , 6, y)
immunoglobulins IgA, IgG, IgM
vascular wall:
elastin [El
collagen [C]
Carbohydrates:
glucose
mucopolysaccharide in vascular wall [M]
Lipids and Fatty Acids:
111
TABLE 10 (continued)
cholesterol (fats): (vitamin F)
free
esteri fied
total
triglycerides
phosphol ipids
total lipids
subcutaneous fat content (insulation) [fat]
effective insulation thickness ofhuman body IT
112
TABLE 11
* VITAMINS
A retinol
B complex:
BI thiamine
B2 riboflavin (component- biotin)
B3 niacin/nicotinamide
B4 adenine
B5 pantothenic acid
B6 pyridoxine
812cholinefolic acidinositolpara-amino benzoic acid PABA
C ascorbic acid
C complexacerolahesperidinrutin
D calciferol
E tocopherol a-, 6-
E complex
K (clotting)
113
TABLE 12
BUFFERING IONS
ammonium NH4 +
bicarbonate HCO 3-
hydrogen (pH) H+
phosphate P04 -
3
sulfate S04 -2
MINERALS AND ELECTROLYTES
calcium Ca
chloride CI
copper Cu
iron Fe
magnesium Mg
phosphorus P
potassium K
sodium Na
TRACE ELEMENTS
cadmium Cd
chromium Cr
cobalt Cb
fluorine F
iodine I
11*4
TABLE 12 (continued)4
protein-bound iodine PBI
lithium Li
manganese Mn
molybdenum Mo
selenium Se
sulfur S
zinc Zn
BLOOD GASES
carbon dioxide CO2
oxygen 02
arterio-venous oxygen concentration difference A[02]I
hemoglobin (percent saturated) Hb
BYPRODUCTS OF METABOLISM
bilirubin
blood urea nitrogen BUN
carbon dioxide CO2
creatine
a creatinine
lactic acid
water
115
Top Related