Monitoring and Control of the Accumulation of Interstitial
Fluid in the Legs
by
MELISSA BARBAGELATA
S.B. Mechanical Engineering
Massachusetts Institute of Technology June 2000
Submitted to the Department of Mechanical Engineering in
Partial Fulfillment of the Requirements for the Degree of
Masters of Science in Mechanical Engineering
at the
BARK
Massachusetts Institute of Technology
MASSACHUSETTS iT
OF TECHNOLOGY
September 2002
OCT 2 52002
C 2002 Massachusetts Institute of Technology
LIBRARIES
All rights reserved
Signature of Author............................
r.
--- I
Melk sa Barbagelata
Department of Mechanical Engineering
. -,June 14, 2002
C ertified by...............................
Hartihiko Harry Asada
Ford Professor of Mechanical Engineering
wji
esis Supervisor
Accepted by.............
..............
Ain Sonin
Professor of Mechanical Engineering
Chairman, Department Committee on Graduate Students
E
Monitoring and Control of the Accumulation of
Interstitial Fluid in the Legs
by
MELISSA BARBAGELATA
Submitted to the Department of Mechanical Engineering on June 14, 2002 in
Partial Fulfillment of the Requirements for the Degree of
Masters of Science in Mechanical Engineering
ABSTRACT
Regardless of its physiological origin, leg edema is a troublesome condition for many
people. Edema in the leg occurs due to an abnormal accumulation of interstitial fluid.
This accumulation can be reduced through certain external physical interactions with the
body. Currently, there is no method for optimizing the prescribed treatments necessary to
reduce edema. Applying closed loop control to the physiological system allows for
regulation of a relevant parameter, such as interstitial fluid. To accomplish closed loop
control it is generally necessary to have a model of the system, to be able to control the
input and to be able to measure significant output variables.
A fully powered massage chair imposes mechanical actuation on the system by changing
the hydrostatic pressure within the body. Experiments done using the chair limit the
treatable subject group to those who experience edema are sitting down. While the
mechanical actuation is applied, a bioimpedance sensor measures the total extracellular
fluid across the legs, which includes the accumulation of interstitial fluid. However,
impedance alone cannot differentiate between the changes due to shifts in venous pooling
or due to shifts in the interstitial fluid. Therefore, a simplified physiological model
specifically built to incorporate the effects of segmental fluid compartments is used to
estimate the contribution to the impedance signal from each of these volumes.
This work presents a new physiological model capable of estimating changes in
interstitial fluid due to gravitational effects. Initial experiments conducted using the
aforementioned massage chair and bioimpedance sensor have aided in both the tuning
and validation of the model. The tuned model is capable of estimating the interstitial
fluid contribution to the impedance signal, providing a means for the quantification and
eventual control of edema.
H. Harry Asada
Thesis Supervisor:
Title: Professor of Mechanical Engineering
2
Dedication
Para Felipe
3
Acknowledgements
As my six years at MIT come to an end, there are many people whom I would
like to thank.
I would first like to thank my graduate advisor Professor Harry Asada for
allowing me to work under his tutelage. He has been supportive and patient
throughout my research endeavors, helping me grow as a researcher. I would
also like to thank him for giving me the opportunity to be his teaching
assistant for 2.010 (Modeling, Dynamics, and Control III), which has been
one of my most rewarding experiences while at MIT.
The research presented here would not have been possible without close
cooperation with Devin McCombie. His insight into the physiological
system as well as his bi-compartmental model is much appreciated. Also
special thanks to Lisa Allison for her help in some last minute experiments.
Thanks to my lab mates in the d'Arbeloff lab who have helped me both by sharing their
ample knowledge with me and by always being such kind friends. Reggie, Eric,
Sam, Kyujin, Phil, Yi and Steve, I will treasure our lab lunches and lab outings.
To all my friends who over the years have always been encouraging and supportive,
especially during the hard times. Reshma, Anjli, Jeff, Nick, Varouj undergrad would
have been a bore without you guys! Thank you, your friendship. Zach, Barbara and
Lorraine, our friendship has endured a whole decade and I look forward to having
you as friends for many more.
All the new people I have met in grad school, it has been a pleasure to spend this last
two years with you, in particular Danielle, Joaquin, Jenny and all the other HST
people, who treated me like I was one of them.
And of course Phil, who has not only been my biggest support but has become my
dearest friend in the last two years. Thank you for being wonderful.
Last but not least thank you to my family. Mami y Papi gracias por todo el apoyo que
me han dado, no seria nadie sin ustedes. Fabrizio and Fressia I hope you guys follow
your dreams, I love you very much.
4
Table of Contents
Monitoring and Control of the Accumulation of Interstitial Fluid in the Legs .................. 1
2
M onitoring and Control of the A ccum ulation of.............................................................
2
Interstitial Fluid in the Legs .............................................................................................
4
A cknow ledgem ents......................................................................................................
5
Table of Contents..........................................................................................................
7
Table of Figures .......................................................................................................
7
Table of Tables .........................................................................................................
8
Chapter 1 Introduction..................................................................................................
8
1.1
Physiological M otivation.................................................................................
9
1.2
Closed loop Control........................................................................................
13
Chapter 2 Physiology: Interstitial Fluid......................................................................
13
Fluid Compartm ents......................................................................................
2.1
15
Fluid shift w ithin a compartm ent...........................................................................
17
Fluid change across m embrane .............................................................................
19
2.2
V enous Pooling.............................................................................................
19
2.3
Edem a ...............................................................................................................
19
Background ...............................................................................................................
20
Edem a dynam ics:...................................................................................................
23
Chapter 3 Sensors and actuations ...............................................................................
23
3.1
Sensors ..............................................................................................................
23
Bioimpedance Sensor.............................................................................................
28
H eart Rate Sensor .................................................................................................
28
Tem perature Sensor ...............................................................................................
29
3.2
A ctuators ...........................................................................................................
29
Chair..........................................................................................................................
30
Other .........................................................................................................................
31
Chapter 4 Understanding the m odel..........................................................................
32
4.1
H um an Body Observer .................................................................................
32
partm
ental
m
odel
...............................................................................
4.2
Bi-com
36
Sensitivity Analysis ........................................................................................
4.3
41
Chapter 5 Implem entation ..........................................................................................
41
D ata Collection .............................................................................................
5.1
41
5.2
Experim ental Setup........................................................................................
43
Experim ental Protocol ...................................................................................
5.3
44
Chapter 6 Tuning the M odel......................................................................................
Chapter 7 A ctuation D ependent Response .................................................................
50
50
Changing leg height ...............................................................................................
51
Com pression .............................................................................................................
Chapter 8 Conclusion .................................................................................................
53
5
8.1
Conclusion about m odel ...................................................................................
Future W ork ......................................................................................................
8.2
References .........................................................................................................................
Appendix A .......................................................................................................................
Appendix B .......................................................................................................................
Appendix C .......................................................................................................................
6
53
54
55
57
59
62
Table of Figures
Figure 1-1: B asic Feedback Loop .................................................................................
Figure 2-1: Major Fluid Compartments and Membranes that separate these
compartments. (modified from Guyton, 1996) .......................................................
Figure 2-2: Flow of fluid into and out of the capillaries...............................................
Figure 2-3: Venous Pressures measured in the reclined and upright positions ............
Figure 2-4: Effect of hydrostatic and colloid osmotic pressure on fluid filtration/reabsorption balance ...............................................................................................
Figure 3-1: Impedance for a cylinder.............................................................................
Figure 3-2: Four electrode Impedance sensor. .............................................................
Figure 3-3: High and Low frequency impedance. (modified from De Lorenzo, 1997.....
Figure 3-4: Resistance and Capacitance Transformation ............................................
Figure 3-5: MEW Real Pro Chair, shown with the legs extended................
Figure 4-1: Bi-compartmental segmentation .................................................................
Figure 4-2: Arterial System (McCombie, 2002)...............................................................
Figure 4-3: Venous System (McCombie, 2002)...............................................................
Figure 4-4: Time Response for output equations using bi-compartmental model.........
Figure 5-1: Electrode arrangem ent ..............................................................................
Figure 6-1: Time Response for fluid accumulation in the legs measured with
B ioimpedenace signal............................................................................................
Figure 6-2: Time Response for fluid accumulation in the legs given by the bicom partm ental m odel.............................................................................................
Figure 6-3: Comparison of impedance signal to model signal ......................................
Figure 6-4: Extracting components to bioimpedance signal.........................................
Figure 7-1: Impedance response to leg position changes. .............................................
Figure 7-2: Effect of compression on fluid in the leg ...................................................
10
15
18
21
22
24
26
27
27
30
33
34
35
38
42
44
45
48
49
51
52
Table of Tables
Table 1: Body Fluid Compartm ents ..............................................................................
Table 2: State variables in bi-compartmental model .....................................................
Table 3: O utput Equations ............................................................................................
Table 4: Sensitivity results.............................................................................................
Table 5: Arterial Blood Pressure measured on the Leg .................................................
Table 6: Lower Blood Pressure for the tuned and un-tuned parameters........................
Table 7: Physiological Model -- Independent Parameters.............................................
Table 8: R esults from Sensitivity Study ...........................................................................
Table 9: Tune independent parameters ..........................................................................
7
14
36
37
40
46
47
57
59
62
Chapter 1
1.1
Introduction
Physiological Motivation
The negative effects of certain physiological conditions could be minimized or prevented
with proper intervention. The initial motivation for this project arose when considering
the recent cases of death associated with deep vein thrombosis (DVT) in airplanes,
otherwise referred to as economy class syndrome. [1] In these cases, a person has died
because prolonged seating resulted in a thrombus, or blood clot, developing in the deep
veins of the calf. [2] The clot formation may have been prevented had the person been
able to walk around and kept the blood from stagnantly accumulating in their legs. While
it is simple to prescribe that people take care to walk around the cabin during long flights,
given the recent number of deaths [3] this method has not proven effective enough.
A second condition whose symptoms can be reduced through external interaction with
the body is edema. Here the motivation is based on an aging lady at a nursing home (or
even at her own home). In certain situations, the lady may be placed in a chair for six
hours at a time without much attention. At the end of this time, an accumulation of
interstitial fluid may have developed in her legs.
Although she may have various
conditions that would make edema more severe, certain maneuvers or sitting positions
could reduce the edema observed.
8
While both the lady at the nursing home and the man in the plane are capable of
preventing or reducing their conditions, they do not. However, if instead of depending on
their own actions they are able to depend on some external actuation to keep fluids, such
as the interstitial fluid and the venous blood from accumulating in their legs, then there
would be less possibility for problems to appear. This could be done through the use of
closed loop control.
1.2 Closed loop Control
Closed loop Control is a familiar concept for the human physiological system. In fact,
the human body utilizes many different feedback loops to maintain internal homeostasis.
Arguably, the most important feedback loops are those which regulate blood pressure,
and those that deal with internal temperature control.
While closed loop control within the body works seamlessly, attempting to integrate
external closed loop control with the human body is not easy. Most interactions with the
body employ open loop control. For example, a doctor prescribes a predetermined pillbased regimen for two weeks. No feedback information is gathered to determine whether
the medicine is having the desired effect.
Similarly, recent inventions such as the
marionette bed [4] are able to turn patients without assistance, but are not able to
determine when it is necessary to perform and action.
The benefits of closed loop control are evident from experience in robotic design. Being
able to feed back a desired value allows careful manipulation of the response. Figure 1-1
shows the key elements of a typical system with closed loop control.
9
Input
Controller
Process
Feedback
Output
1
.4
Figure 1-1: Basic Feedback Loop
In this case, the process (often referred to as 'the plant') is the human physiological
system, the controller will be the source of actuation, namely an automated chair, and the
output to be fed back will be interstitial fluid indirectly measured with a bioimpedance
sensor.
Without feedback, control is based on estimated responses.
For instance, reexamining
the marionette bed, a nurse knows that it is important to turn a patient say every 4 hours.
Though she may not know the exact state of the body during this period, she will still
perform the prescribed action.
The goal of this project is to set up a system that is able to monitor a physiological state
in a person, focused on interstitial fluid in the legs. Since this desired state cannot be
measured directly, a model must be set up to estimate the contribution of this variable to
the measured signal. Then, actuation is used to maintain or impose a desired value for
such physiological state.
A system of closed loop control has been successfully accomplished in the rateresponsive pacemaker. [5] This device is able to monitor a variable such as a person's
breathing rate and impose a heart rate that corresponds with such a breathing rate. The
10
pacemaker effectively controls the heart rate because it is implanted inside the body and
acts directly on the heart muscle that determines the contraction of the ventricle.
Many physiological states can be manipulated externally. For instance, diabetic patients
can control the level of glucose in their blood by regulating how many sweets they eat,
though much more sophisticated work has been done to automate this process. Chemical
regulation of internal parameters is a very common way of imposing control upon the
physiological system. Another way of imposing control is through thermal interaction.
For example, the body's internal temperature can change depending on how many layers
of clothing are used by a person. Finally, mechanical actuation can also affect certain
states of the physiological system. Exercise can change the cardiac output, stroke volume
and body temperature. Even postural changes can alter certain internal parameters.
When designing closed loop control for the physiological system it is necessary to find a
parameter that can be controlled through external actuation. Even more importantly,
though perhaps not as limiting, as finding a parameter that can be non-invasively
controlled, is finding one that can be non-invasively monitored.
Non-invasive
monitoring technology has made significant developments in recent history. Through
technological advancements in ultrasound, photo-plethysmography, bioimpedance and
others, many more physiological states can be measured non-invasively than before.
Finally, in order to accomplish closed loop control once the appropriate sensors and
actuators have been selected, the system to be controlled must be fully understood. To
accomplish this a model is created that is able to estimate the characteristics that are
relevant in the control of the chosen physiological states. Ideally, the model should run
11
parallel to the real system, and its predictions should match the observed physiological
states. Before the model matches the real system, it may be necessary to tune the model
parameters.
12
Chapter 2
Fluid
Physiology: Interstitial
It is important to understand the physiological characteristics that are relevant to the
conditions that will be controlled. Since the focus will be on the control of interstitial
fluid in the lower extremities and how it affects edema, the dynamics of fluid
accumulation in the legs is most relevant. First, an anatomical description of the fluid
distribution in the different compartments of the body is discussed. Then, the dynamics
that give rise to edema are presented
2.1 Fluid Compartments
Water makes up between 55 - 60% of the total body mass of the average adult. Even
though this water exists everywhere in the body, it is can be separated into two major
components. Water that lies inside the cells is referred to as intracellular fluid (ICF) and
water that lies outside the cells is referred to as extracellular fluid (ECF).
The
extracellular fluid can be further divided into the water that exists in the plasma, the
interstitial space, the fluid in the bones and other dense connective tissue, and
transcellular fluid. Table 1 illustrates the percentage composition of each of these
compartments.
13
Table 1: Body Fluid Compartments [61
Body Weight
Total Body
Volume
[%]
[Liters]
Water
[%]
ICF
33
55
23
ECF
27
45
19
Plasma
4.5
7.5
3.2
Interstitial
12
20
8.4
Dense CT water
4.5
7.5
3.2
Bone water
4.5
7.5
3.2
Transcellular
1.5
2.5
1.5
60%
100%
42 liters
TBW
Even though dense CT water and bone water make up a fairly large percentage of the
extracellular water, because the fluid moves very slowly within and across these spaces
they can essentially be considered as constant, and unimportant when considering the
effects of fluids flowing across membranes. On the other hand, the fluid in the plasma is
constantly moving and interfacing with the fluid in the interstitial space. Therefore, these
fluid compartments can be simplified into the major reservoirs, the intracellular fluid and
the extracellular fluid consisting of the interstitial space and plasma. This distribution is
shown in Figure 2-1.
The interactions within and across these compartments will be
further discussed.
14
.....
------
...
.
.. ..
. ....
....
....
Figure 2-1: Major Fluid Compartments and Membranes that separate these compartments.
(modified from Guyton, 1996) [7]
Fluid shift within a compartment
The fluid compartments shown in the figure above are present over the entire body.
When looking at a particular body segment there will be contributions from each of the
compartments. For instance, when looking at a segment of the leg, there will be water
found in the intracellular, interstitial and vessel compartments. Therefore, when studying
the fluid shifts within a compartment, the shift actually occurs between different
segments of the body, as will be discussed below.
15
PLASMA
Plasma is the only fluid compartment that exists as a real collection of fluid in one
location [6], namely in the blood vessels. This fluid is continuously pumped by the heart
to all parts of the body. Normally an equal amount of blood is pumped into an area by
arteries and carried back to the heart by the veins. However, certain postural changes
will affect this balance. When a person stands up from a reclined position the effect of
gravity causes a rapid fluid shift from the thoracic venous blood into the leg venous
blood. This shift can be as large as 500 - 700 ml, which is then pooled in the veins of the
leg [8]. Such drastic changes will result in an instantaneous reduction of cardiac output.
However, an intact cardiovascular system should recover quickly.
These changes in venous blood, though not as dramatic, are also evident when a person
moves their legs from the downward position to a horizontal position and vice versa.
Another factor that affects the volume accumulation in the legs is temperature.
Temperature is particularly important when looking at fluid transfer in the peripheral
system. In the legs, temperature drops will be related to the vasoconstriction of the blood
vessels. Therefore, even if the core temperature of the body has not changed, the external
temperature of the legs will have an effect on how much blood is being stored within the
leg veins.
The primary contribution to shifts in the plasma distribution is attributed to changes in
fluid stored in the veins. This is because the capacitance of the veins is very large and
can be changed to accommodate more fluid. The arteries, on the other hand, have a much
16
smaller capacitance. Therefore, the amount of fluid stored in the arteries will not change
under normal conditions.
INTERSTITIAL
Since the interstitial fluid is not able to move as freely as plasma, fluid changes within the
interstitial space are not as significant. Instead, fluid changes between the interstitium
and plasma are of more importance. These are discussed in the following section.
Fluid change across membrane
During normal conditions the total fluid leaving the capillaries is equal to the fluid
returned to the capillaries plus the fluid carried back to the circulatory system through the
lymphatic system, as shown above.
When this balance between influx and out flux is altered, there will be a change in the
fluid accumulation.
The two general causes of extracellular edema are: (1)
abnormal
leakage of fluid from the plasma to the interstitial space and (2) failure of the lymphatics
to return fluid from interstitium back to the blood. [9] This discussion focuses on the
leakage of fluid from the plasma to the interstitial space.
17
VENULE
ARTERIOLE
0
0
CAPILLARY
Less Fluid
Returns
Fluid
Leaves Capillary
Figure 2-2: Flow of fluid into and out of the capillaries
The net transfer of fluid across the capillary wall is defined primarily by four forces.
These forces combine in the following way to form the Starling hypothesis:
F = K[(P- PJ)- (uz,- )z )]
(Eq 1)
Which states that the difference between capillary pressure, P, and interstitial fluid
pressure, PI , minus the difference between plasma colloid osmotic pressure, 71 ,, and the
interstitial fluid colloid osmotic pressure z,, scaled by the capillary filtration coefficient,
K , which is the (the product of the specific permeability of the capillary times the
surface area of the capillaries) determines the net flow into the interstitium, F . F is
defined to be positive when there is a net outward flow of fluid from the capillary.
Changes in any of these forces will affect the flow of fluid from the capillary.
18
2.2
Venous Pooling
When a person changes from a reclined position to a standing position, blood stored in
the veins of the chest and abdomen moves to the veins in the legs due to the change
gravitational forces [8]. When this occurs the body responds as if it had just experienced
a small hemorrhage including a drop in arterial pressure. If a person remains standing,
the without movement the extra blood will remain in the legs. However, as a person
begins to move this extra blood will reenter circulation, since the pumping action of the
leg muscles will force fluid back towards the heart and out of the leg veins.
Since the concern of these experiments is limited to changes that occur while sitting
down, the pressure drops that may arise from standing and lead to conditions such as
orthostatic hypotension [10] are ignored. Nevertheless, as the relative position of the legs
to the heart changes while sitting down the volume of blood stored in the veins will also
change.
2.3 Edema
Background
Edema refers to an abnormal build up of fluid in the tissues of the body. It can occur in
several parts of the body including the lungs and the upper and lower extremities. When
edema occurs in the legs it may have several causes. In the healthy individual, swelling
occurs as a result of prolonged standing or sitting. [11] In addition, edema may be a sign
of the presence of a serious disease. For instance, congestive heart failure will decrease
the effectiveness of the heart's pumping, resulting in build up of fluid that is visible in the
feet and ankles. Also, severe chronic lung disease will increase the pressure in the blood
19
vessels to the lungs. This pressure backs up to the right heart and ultimately to the veins
emptying into the heart causing swelling in the feet and ankles.
Since edema often indicates a serious condition, it is fundamental to understand the cause
of edema when addressing its treatment. However, there are certain actions that can help
the fluid in returning the veins and the lymphatic channels. [12]
These actions will
alleviate the discomfort and pain often associated with edema, even though they are not
directly addressing the source of the problem. [13] Elevating the legs so that they are
higher than the chest will help reduce the accumulation of fluid in the legs. Additionally,
light exercise will cause a pumping action of the muscles. The compression of the legs
will also help to keep the fluid inside the vessels. A common therapy to help alleviate
edema while standing is the use of medial compressive stockings. [14]
Edema dynamics:
Edema occurs when there is an abnormal accumulation of fluid in the interstitial space.
Looking back at Starling's Hypothesis, a positive value of F would cause an
accumulation of fluid in the interstitial space. Many conditions can affect each of the
factors contributing to flow across the capillaries.
Bacterial infections, vitamin
deficiency or burns can affect capillary permeability, Kf . Plasma Protein concentration,
rp,, is decreased due to loss of proteins in urine and failure to produce proteins as is the
case in liver disease. Capillary pressure, P, is influenced by excessive kidney retention
of salt and water, high venous pressure, and decreased arteriolar resistance. [7]
20
HYDROSTATIC PRESSURE
The factors mentioned above which disturb Starling's equilibrium all occur over longer
periods of time. In addition, there is another transient factor that affects capillary
pressure, namely gravity, see Figure 2-3.
-42
2 +90
Venous Pressure [mmHg]
5
2
Figure 2-3: Venous Pressures measured in the reclined and upright positions[15]
Gravity will have noticeable effects on the vascular pressures and volumes in various
parts of the body, depending on the vertical distance of the column of blood from the
heart. This increase in venous pressure will also raise the pressure in the venules and
eventually in the arterial end of the capillary; this will result in an increase of filtration
across the capillaries, and an increase in the accumulation of fluid in the interstitium [15],
see Figure 2-4.
21
40
40
PA
P
OW
30
30
20
20
10
10
P
b) Increased Venous Pressure
a) Normal
Figure 2-4: Effect of hydrostatic and colloid osmotic pressure on fluid filtration/re-absorption
balance [151
Although there are many other factors aside from those listed that will affect the Starling
balance, it is assumed that under normal conditions for P, A , and ,z will be operating at
steady state. On the other hand, the transient effects of posture on P cannot be ignored;
instead, they can be used to control the accumulation of fluid in the interstitial space.
22
Chapter 3
Sensors and actuations
3.1 Sensors
Bioimpedance Sensor
IMPEDANCE MODEL
The principle of electrical-impedance is based on measuring electrical conductance to
assess body volume changes. Bioimpedance has been used to measure many different
types of biological electrical conductors, an ultimately to assess important physiological
parameters.
A few common ones include: total pulmonary function, cardiac output,
segmental blood pulsation, and segmental venous reservoir. Bioimpedance is based on
the fact that a small current can be safely introduced into the body. Then, by measuring
the voltage imposed by the current between two points, it is possible to deduce the
impedance of a particular area. For a cylinder, a simple model relating impedance to
volume is shown below.
23
Z=p a
z
Z=p-
(Eq 2)
zA
(b)
(a)
Figure 3-1: Impedance for a cylinder
Where Z is the impedance measured across the cylinder, p is the resistivity of the matter,
a is the cross sectional area, I is the length and V is the volume. If the length of a body
segment remains constant the expansion of a blood vessel results in an increase in its
cross sectional area and therefore volume [16]. This change in volume can be measured
using bioimpedance.
The volume change is modeled as an additional impedance in
parallel to the first. Assuming that the measured length is constant, the change in volume
is due to a change in the vessel's cross sectional area. The following was derived by
Nyboer [16].
24
AZ=Zi-Z2
(Eq3)
=p_)012
V
AZ - -
2
P1
V2
AV
V1V2
plAV
ZAV
V2
V
AZ- -AV
Z
V
(Eq 4)
Thus, the fractional change in impedance is inversely related to the change in volume. In
other words, as the volume increases, the impedance decreases and its inverse, the
conductance, increases.
SENSOR MECHANICS
The Quantum X from RJL Systems, Clinton Township, MI was used for Bioelectrical
Impedance Analysis (BIA). The Quantum X is a four-electrode sensor. This means that
the current flows through the two outer electrodes and the voltage is measured at the two
inner ones, see Figure 3-2. Two-electrode configurations are also possible. However,
when the voltage is measured at the same location the current is applied the quality of the
resulting signal is poor.
25
...........
...
Smiusaidal constant acrrent source
AC vector
referece
Resstance
0 degree
s
Reactance 90 dgre
I
D~ei~
Selectroe
Current swrce electrode
Current source electrode
Measured
biological resistance
and reactance
Figure 3-2: Four electrode Impedance sensor. [171
The Quantum X operates at a frequency of 50 kHz and inputs a current of 800 uA into the
body. The voltage drop between the two inner electrodes is measured through an input
impedance amplifier. At this frequency the measured impedance has contributions from
both resistive and reactive elements. The resistive component is due to the extracellular
fluid, while the reactive contribution is due intracellular fluid, since the cells in the body
act like capacitors because of their cell membrane. At low frequencies, the current is
unable to penetrate the cells. As the frequency increases though, some of the current is
able to pass through the cells. At very high frequencies, all the current would go through
the cells [18]. See Figure 3-3.
26
High Frequency Current
(3)ID
Cell Membrane
Intra-Cellular Water
Extra-Cellular Water
Low Frequency Current
Figure 3-3: High and Low frequency impedance. (modified from De Lorenzo, 1997
At a frequency of 50 kHz, measurements of the phase angle between the input and the
resulting voltage can separate the resistive and reactive components of the response. The
Quantum X, computes the reactance and resistance as if they existed as a simple resistor
and capacitor in series. Since the corresponding biological model is of a resistor and
capacitor in parallel, the data acquired must be converted into its parallel equivalent
through the following transformation:
Resistance and Capacitance in Series
Rpa, = Rseries +
cr
Resistance and Capacitance in Parallel
X~
Xc,par =Xcsre,+
=Xc,series
R2
XR,,,,xc
eie
Xc,series
Figure 3-4: Resistance and Capacitance Transformation
SEGMENTAL MEASUREMENTS
For full body impedance measurements using the Quantum X the electrodes are placed at
the wrists and at the foot creating a full loop of current throughout the body. However,
27
since the focus of this project is the volume accumulation across the legs, the electrodes
were placed at the foot and immediately below the knee. Such a method of segmental
impedance measurements will be more accurate when estimating extracellular fluid in a
confined area than the full body method. [19] In addition, because the geometry of this
area is simple, it can be approximated with the simple cylindrical model described above.
The resistive component to the impedance will include contributions from each of the
fluids that make up the extracellular space as shown in Table 1. However, since only the
interstitial fluid and vessel plasma will respond to dynamic changes the other
contributions can be considered as adding to the DC component of the impedance signal
but not to the changes seen.
Heart Rate Sensor
The heart rate sensor used is the Nellcor N-395. It is able to measure both the heart rate
and oxygen saturation at the fingertip. It uses photo-plethysmography to methods to
calculate the heart rate. Alternatively, the Ring Sensor [20], can also be used to noninvasively measure the heart rate.
Temperature Sensor
A simple thermistor is calibrated and used to record the temperature of the foot during
experiments.
These external temperature measurements
can reflect the degree
vasoconstriction or vasodilation in the leg. Since, as described earlier, both of these
affect the amount of venous pooling.
28
3.2 Actuators
Chair
In order to control on a physiological state actuation must be able to affect the state of the
body variables.
Chapter 2 shows how both interstitial fluid accumulation and venous
pooling are affected by a change in hydrostatic pressure.
Therefore, by externally
changing the hydrostatic pressure it is possible to change the states of both of these
parameters.
The Real Pro massage chair form Matsushita Electric Works, Ltd (MEW) was utilized for
conducting experiments.
The Real Pro chair is capable of conducting a series of
automated, mechanical massage routines, which include the compression of the lower
calves and ankle area. All of the components of the chair are fully powered, including
the leg rest, which has a range of movement from-5 0 to 850 measured from a line
perpendicular to the ground. It shall be noted that, the calf and ankle compression can be
performed independent of all other actions.
29
Figure 3-5: MEW Real Pro Chair, shown with the legs extended
Other
Besides mechanical actuation, several other forms of actuation were considered.
In
particular, when considering fluid accumulation in the legs, passive electrical stimulation
of the leg muscles would stimulate some of the fluid pooled in the veins to be sent back
to the heart, through the pumping action of the muscles. Electrical stimulators can be
placed over the leg muscles and have been approved by the FDA to improve blood flow.
[21]
30
Chapter 4
Understanding the model
The resistive signal that the bioimpedance sensor outputs includes contributions to the
extracellular fluid from plasma in the blood vessels, interstitial fluid and other fluids.
However, as previously discussed in Chapter 2, it is the interstitial fluid and the venous
blood which will be most likely have large variations. As a result, the extracellular fluid
can be modeled as being composed of only venous blood and interstitial fluid. Then, the
changes observed with the impedance signal will be due only to changes in these two
compartments.
When analyzing the effect on a particular physiological condition such as edema, it is
important to separate the relative contributions from interstitial fluid and venous pooling.
This can be done by taking advantage of the fact that the volumetric changes for each
have inherently different time constants. On the one hand, fluid shifts within the venous
system happen almost instantly. On the other hand, fluid movement into and out of the
interstitium takes place over significantly longer time periods.
By manipulating the
hydrostatic force applied to the system, it is possible to separate the effects from each of
the different fluidic volumes. In order to clearly differentiate between each of these, a
model is created that incorporates the necessary parameters to define these state
variables.
31
4.1 Human Body Observer
The Human Observer is a major undertaking by McCombie and Asada to create a
continuous real time model of the human physiological system. It is based on a two-part
simulation model made from a continuous model which refers to a discrete model for
parameter validation. The initial discrete model is based on the agent based Mori model
[22], which itself is based on the Coleman model. This model contains 25 subsystems
and is able to calculates hundreds parameters.
It includes information from the
circulatory, respiratory renal and hormonal systems. One of the purposes of the Human
Observer is to be able to impose certain conditions on the model to see how the real body
would react by observing how the output variables of the model change. For example,
one of the modules in the Human Observer is an exercise stimulus. Using this module, it
is possible to see the effect of exercise on heart rate, blood pressure and other variables.
At the same time, actual data is collected from the human and can be used to tune and
validate the model for different subjects.
The human observer separates the body into 11 segments based on their location in the
body and calculates the circulation for all the segments simultaneously while taking into
account any additional influences due to physical location. [23]
4.2 Bi-compartmental model
The bi-compartmental model is a reduced version of the full Human Observer. Instead of
separating the body into eleven segments, it separates it into only two major segments.
The upper compartment includes the contribution from the head, the upper extremities
and the torso, while the lower compartment includes the circulation only in the legs. This
32
architecture is chosen specifically to be able to model the effects that position changes
have on the dynamics of the lower extremities. In particular, the circulatory changes that
affect interstitial fluid are incorporated into the model since it is expected that these will
yield important information to help prevent edema.
UPPER BODY
(TRUNK, ARMS, & HEAD)
LOWER BODY (LEGS)
Figure 4-1: Bi-compartmental segmentation
McCombie created the bi-compartmental model using bond graphs to independently
represent the flow within the arterial and the venous systems. The two branches of the
bond graph are connected by including the parameters calculated in the model of the
microcirculation for each segment, as shown in the figures below.
33
ARTERIAL SYSTEM
UPPER BODY
(TRUNK, ARMS, & HEAD)
ARTERIAL CAPACITANCE
C
UPPER BODY
ARTERIAL RESISTANCE
UPPER BODY
AORTIC
CAPACITANCE
I SF
| 0
SE
R
ARTERIAL RESISTANCE
R
LOWER BODY
ARTERIAL CAPACITANCE
LOWER BODY
C -
ISF
10
C
J_
-
1
SE
0
' SF
I
MICROCIRCULATION
UPPER BODY
GRAVITATIONAL PRESSURE
ON UPPER BODY
LEFT VENTRICLE
FLOW SOURCE
GRAVITATIONAL PRESSURE
LOWER BODY
MICROCIRCULATION
LOWER BODY
LOWER BODY (LEGS)
Figure 4-2: Arterial System (McCombie, 2002)
34
VENOUS SYSTEM
UPPER BODY
(TRUNK4 ARMS, & HEAD);
MICROCIRCULATION
VENOUS CAPACITANCE
UPPER BODY
VEIN WALL
DAMPING
0UPPER
BODY
R
I
VENOUS RESISTANCE
UPPER BODY
GRAVITATIONAL PRESSURE
ON UPPER BODY
VENA CAVA
CAPACITANCE
RESPIRATION
SE
0
VEIN WALL
DAUPING
-
1
-
R
VENOUS RESISTANCE
LOWER BODY
R
'
-
R
-
1
PRESSUR
C.
HEART VALVE
RESISTANCE
SE
1-
RIGHT HEART
CAPACITANCE
GRAVITATIONAL PRESSURE
LOWER BODY
VEIN WALL
DAMPING
R
VENOUS CAPACITANCE
LOWER BODY
C
0
Is F
MICROCIRCULATION
LOWER BODY
LOWER BODY (LEGS)
Figure 4-3: Venous System (McCombie, 2002)
The bi-compartmental model contains nine state variables. Seven of the variables are
associated with each of the capacitances shown in the bond graphs above, while the other
two are found in the microcirculation that links the arterial and venous systems to both
the upper and lower segments. The state variables of the model are shown in Table 2.
35
Table 2: State variables in bi-compartmental model
State Variable
Parameter name used in MATLAB
Aortic volume
Q1
Artery volume, lower
Q2
Artery volume, upper
Q3
Vena cava volume
Q4
Vein volume, lower
Q5
Vein volume, upper
Q6
Interstitial volume
Q7
Interstitial volume
Q8
Volume of the right atrium
Q9
MATLAB* is used to solve the differential equations of the bi-compartmental model. In
order to obtain the time profile for each of the state variables above, thirty-four
independent parameters and nine initial conditions are necessary.
These parameters
include: compliances which are calculated from known values, resistances which are
estimated from a known range, and other measurable characteristics such as height of
heart, inspiration rate, and heart rate. [23] All of these parameters are ultimately required
to obtain an accurate time profile of the output equations.
When performing the model
simulation a specific value must be used for each parameter. The chosen values represent
a typical value for each parameter; however, they have not yet been tuned to a particular
person. The values used are given in Appendix A and will be hereafter referred to as the
base values.
4.3 Sensitivity Analysis
Since it is very difficult to keep track of so many parameters at once, a sensitivity
analysis was performed in order to determine how each parameter affects the chosen
36
outputs. First, the output equations were specified to incorporate the measurements that
are of most interest, as shown in the Table 3.
Table 3: Output Equations
Output Variables
Aortic pressure
Arterial pressure (lower)
Output Equation [state variables]
= (Qi/Cal), Cal is the aortic compliance
= (Q2/Ca2), Ca2 is arterial compliance (lower
body)
Venous volume (lower compartment)
= Q5x106
Interstitial fluid (lower compartment)
= Q7x106;
The four output functions are the aortic pressure, arterial pressure in the legs, the fluid
shift in the legs and the interstitial fluid shift. Notice that the sum of the third and fourth
output variables is the extracellular fluid in the lower compartment. This sum can be
directly measured using the bioimpedance signal. Since these output equations yield a
time profile response, it is necessary to extract certain characteristics that can be used to
compare whether the response is accurate or not. The time profile for each of the state
variables will be a straight line, unless some disturbance is introduced into the system.
Here, the disturbance introduced is a step change in the position of the legs, which
changes the hydrostatic pressure in the legs. The time response for each output can be
seen in Figure 4-4.
37
Figure 4-4: Time Response for output equations using bi-compartmental model
Notice that the output variable may respond in one of three distinct ways. The lower
arterial blood pressure (Q2) and lower body venous volume (Q5) each show a step
change in the output response due to the step disturbance. Consequently, the initial and
final systolic and diastolic values are necessary to define the response. The aortic blood
pressure (Qi) shows a transient response to the disturbance, making only the final value
of the systolic and diastolic pressures and the depression (or 'dip') relevant. Finally, the
lower interstitial volume (Q7) has a ramp response to the disturbance, making the slope
the relevant characteristic for this output variable.
With this information, it is possible to extract one, three or four values that will
completely describe each of the output equations. These values will serve for comparison
38
in the sensitivity analysis.
Since now, it is unnecessary to compare the entire time
response. The sensitivity metric is based on the following equation:
outputextracted value
Eq 5.
apparameterbase value
Where
8
aPparameterase valuerepresents
poutput extracted value
how much the base parameter has been changed and
represents how much extracted output value has change as a result of the
change in base parameter. The result of this calculation reflects the influence of changes
in the independent parameter on the chosen output variable.
The complete set of
calculations, as well as all the sensitivity values for all parameters are found in Appendix
B.
The closer the sensitivity metric is to zero, the smaller the influence of the independent
parameter is on the output. After performing the sensitivity analysis, we find that it is
reasonable to keep track of a much smaller number of parameters for each output
variable. These parameters are shown in the following table.
39
Table 4: Sensitivity results
"*"UaP as
Output Variable
Independent parameter
Aortic pressure
Stroke volume (SV)
0.93
Heart rate (bpm)
0.72
Arterial resistance (Rart2, Rart3)
0.44
Stroke volume (SV)
0.45
Heart rate (bpm)
0.35
Heart height
0.61
Blood density (rho)
0.51
Compliance veins (C:v)
0.99
Heart height
1.02
Blood density (rho)
0.85
Heart height
1.17
Blood density (rho)
0.99
Bulk Flow Resistance (lower body)
capillary to interstitium (Rbf2)
-0.70
Molar concentration of protein in the
blood (Cb)
-0.32
Arterial pressure (lower)
Venous volume
(lower comp.)
Interstitial fluid
(lower comp.)
autaPbase
The last column of the table shows the influence of each independent parameter on the
output variable, the larger the number the greater the relation between the parameter and
the output. Negative numbers indicate an inverse relationship. The parameters chosen
have sensitivity measurements of higher than 0.30.
40
Chapter 5
Implementation
Once the relationship between internal independent parameters and the output equations
is established, the information can be used to analyze our experimental results. The
initial set of experiments was chosen so that the characteristics observed in the model can
also be seen in the experiment. This chapter will describe the experimental setup as well
as the initial investigational results.
5.1
Data Collection
The Quantum X used in the experiments was specially modified by RJLSystems to
provide an analog output for both the resistance and reactance components of the
impedance signal.
The impedance analyzer displays a digital signal in the range of
1 50Q for the lower leg, with resolution of ±0. IQ. The equivalent analog signal has a
voltage of 0.150 V.
The analog signal is amplified, using an operational amplifer,
before being sampled by a National Instruments DAQ card (6024E). The data collection
is controlled through a simple GUI written using LabView, and later analyzed offline
using MATLAB® version 6.1.
5.2
Experimental Setup
The Quantum X bioimpedance sensor described in Chapter 3 measures the impedance
imposed by the body across the distance established by the two inner electrodes. In body
composition analysis, the electrodes are placed on the feet and wrists, so that the
41
.
.........
impedance can be measured across the entire body. However, since our experiments
focus on measuring the volume accumulated in the leg, a couple of different electrode
arrangements are possible. The impedance could be measured across the entire leg, or it
could be measured only across the lower leg, as shown in Figure 5-1.
The blocks
represent the electrode placement; the letter i shows where the current was introduced
and the letter v shows where the voltage was measured.
Figure 5-1: Electrode arrangement
Both of these arrangements provide similar information, since the experiments focus on
measuring fluid accumulation. In fact, since the area between the knee and the waist
remains stationary, there are no dynamic changes associated with this volume. When
each was tested, the primary difference was that the configuration on the left was easier
42
to position and more comfortable to use. Therefore, the knee-ankle arrangement was
chosen. Care was taken to place the electrodes on the same location each time, as shown
in the figure above.
5.3 Experimental Protocol
As previously stated, the focus of the experiments is on temporally-based fluid
accumulation in the legs. There are several factors, discussed in Chapter 2, that affect
this volume, but for the initial experiments the focus is on isolating the effects due to
gravitational changes, i.e. changes in hydrostatic pressure.
It is expected that after a change in the leg position there will be an initial change in the
measured fluid volume due to the fluid shift within the vessels and a secondary
contribution due to fluid shift between the capillaries and interstitial space. [24] This is
believed to be true since the interstitial fluid shift occurs over a longer period of time,
with a slow time constant.
Ideally, the subject tested will not have any abnormal
interstitial fluid accumulation before beginning data collection. Therefore, it is important
for the subject to have been in an active situation immediately before sitting in MEW's
Real Pro Chair, i.e. the subject should not have previously been sitting elsewhere for a
long period of time.
Once seated, the legs are raised and extended. Approximately two minutes later, the legs
are moved into the gravity dependent position. The impedance signal is measured for the
next twenty minutes. Special care is taken not to move the legs during that time, nor to
contract the leg muscles, since both of these will affect the impedance signal.
43
Chapter 6
Tuning the Model
The initial set of experiments was aimed at tuning the model described in Chapter 4.
Data was collected on a subject following the guidelines in the experimental protocol
outlined in the previous chapter. In the first step of the data analysis, only the resistive
contribution to the bioimpedance signal was plotted, as shown in Figure 6-1.
160Flat region
158
156
Rapid movement of
blood
rl 14venous
E'154 0
a 152 -
Linearly increasing
fluid amount
i 150.
0-148
E
146 144
142
I
200
I
400
I
600
I
800
I
1000
I
I
I
1200 1400 1600
time [seconds]
Figure 6-1: Time Response for fluid accumulation in the legs measured with Bioimpedenace signal
Notice in the figure above that the measured impedance signal is initially flat. After
about 160 seconds, the legs are moved towards the downward position. At this point,
44
there is a very rapid drop in the impedance due to the venous blood moving into the legs.
Over the next 30 minutes, there is a fairly constant accumulation of fluid, denoted by the
decreasing impedance. The data acquired from the experiment can be compared with the
data generated by the bi-compartmental model discussed in Chapter 4. The relevant
output equation for this comparison is the sum of the interstitial fluid shift and the venous
blood shift. The model simulation for this volume accumulation is shown below.
Fluid Volume Lower Legs
j9$uu
3850 3800 -
3750
' 3700
3650
36003550
350-n
0
I
200
I
400
I
600
I
I
800
1000
I
1200
I
I
I
1400
1600
1800
2000
time (sec)
Figure 6-2: Time Response for fluid accumulation in the legs given by the bi-compartmental model
The response shown in the figure above is obtained using base values for all of the
independent parameters. In order for the simulation to provide information about the
45
subject from whom the data was taken, the parameter values in the model must be
properly tuned.
Parameter tuning requires additional measurements to be taken. Measuring the output
variables established in Chapter 4 will make it possible to tune the parameters that have
been shown to have a high influence on each output variable. The arterial blood pressure
can be measured in the upper body as well as the lower body. Though this measurement
is not taken continuously throughout the experiment, it does add information about the
points that have been extracted from the model. The following table shows the pressure
readings taken at the leg.
Table 5: Arterial Blood Pressure measured on the Leg
Systolic
Diastolic
Legs up
125 ±2
70± 2
Legs down
155 ±2
92± 2
The pressure measurements shown above were taken by a nurse at the feet using a cuff
and stethoscope, the accuracy provided refers to the accuracy using this method
repeatability.
Each measurement was done several times to ensure accuracy and the
averages are shown above.
In addition, there are other parameters that can be directly measured and inputted into the
model. The heart rate is measured continuously with a Nellcor sensor. Since there were
no significant heart rate changes, the measured average of 68 beats per minute was used
in the simulation. Also, the position of the heart and the legs were measured and used in
the model, all of these values are shown in Appendix C. The following table shows the
46
output values for the lower blood pressure both for the pre-tuned parameters and for the
tuned parameters.
Table 6: Lower Blood Pressure for the tuned and un-tuned parameters
Blood Pressure
Measured
Simulated Base
parameters
Simulated Tuned
parameters
Legs Up
125
91
115
Diastolic
70
57
82
Legs Down
155
186
162
92
152
128
Systolic
Systolic
Diastolic
The information acquired from the blood pressure measurements and the other measured
parameters allowed us to tune some of the parameters in the model, including, leg height,
heart height, heart rate, and arterial resistance.
However, in order to produce more
numerically relevant information using the model, more parameters should be tuned.
Additional information can be extracted from the impedance measurements.
For
instance, the total decrease in impedance over the entire experiment can be measured.
With this information, more parameters can be tuned, including venous compliances,
right heart compliance and bulk flow resistance.
The result is a much better match
between the signal measured by the impedance sensor and the signal simulated by the
model. The following figure compares the impedance signal converted to a volume with
the volume signal from the model.
For a complete list of the tuned parameters, see
Appendix C.
47
3800
3750-
simulated signal
, 3700-
3650-
measured signal
E
-
0
3600-
3550-
3500'
0
500
1000
1500
2000
2500
time [seconds]
Figure 6-3: Comparison of impedance signal to model signal
Now that the model signal is able to provide an acceptable match for the measured data,
it is possible to extract the contributions from the interstitial fluid and from the vein to the
fluid volume in the lower legs, as shown in Figure 6-4.
When determining levels of interstitial fluid accumulation that are dangerous for edema,
the interstitial fluid shift, not the venous blood shift should be examined.
48
Fluid Volume Lower Legs
3750
-
3700
3650
E 3600
-
05
3550
35000
200
400
600
800
1000
1200
1400
1600
time (sec)
Lower Body Interstitial Volume
3600
I
I
I
I
I
I
I
I
I
I
I
I
1800
2000
I
3580
-J
E
3560
3540
E
.0 3520
3500
3480'
0
I
200
400
600
800
1000
1200
1400
I
I
1600
1800
2000
1600
1800
2000
time (sec)
Lower Body Venous Volume
1501i
E 100 F
E
.5
I
I
I
200
400
600
50
800
1000
1200
1400
time (sec)
Figure 6-4: Extracting components to bioimpedance signal
49
Chapter 7 Actuation Dependent
Response
So far, the information obtained from the model has been compared to data obtained from
the subject following a specific protocol. In order for closed loop control to be possible,
the response of the human subject to actuation imposed by the chair must be understood.
Changing leg height
In order to record the applied actuation the chair was modified by attaching a low
friction, rotary potentiometer to the leg lifting mechanism.
This sensor allows for
simultaneous collection of data related to both leg position and impedance changes.
Lowering and raising the position of the legs relative to the heart changes the
bioimpedance signal. These changes primarily affect the venous blood in the vessels,
which is evident from the initial fast response of the signal to the input.
50
- -_:_
-""'
L
= -
-.- .---
.........
-. .....
-- -
I
I
140
Impedance
Chair Angle
135
E
-13
125F-
120
7
B2M
W4
.f
Time [s]
8
em
9WO
920
94
Figure 7-1: Impedance response to leg position changes.
Figure 7-1 shows the resistance signal as well as the output from the potentiometer
relating chair position signal.
The close correlation between resistance and position
shows that the response of venous pooling occurs at the same time as the input is applied.
Therefore, the change in venous pooling can be considered instantaneous.
Compression
The other primary actuation that can be imposed by the MEW chair is sinusoidal
compression of the lower leg from the calf to the ankle. The response to this actuation is
shown below.
51
186
Change in baseline
fluid volume
15
175
165
-
111111' 11110111
-L
I
I
1900
190
160
17M
176D
lam5
19w
Time Isecon1sl
3101
2001
Figure 7-2: Effect of compression on fluid in the leg
The intermittent compression pumps fluid out of the calves, but some fluid returns when
the compression is released. The interesting thing to note is that the final value of the
impedance is higher at the end of a series of compression. This implies that the net
amount of fluid in the leg was actually changed through compression. By understanding
the effect of similar actuations, it may be possible to change the state of the body.
52
Chapter 8
8.1
Conclusion
Conclusion about model
The model is vital to the analysis of information acquired from the sensor. The simple
model presented here is capable of displaying internal parameters that may not be readily
available directly from the sensor.
This linear model provides a good first order
approximation for estimating the amount of interstitial fluid in the body from the
impedance signal.
Tuning the parameters of the model helps ensure better agreement between the model and
the real data, the more parameters that can be tuned the better the model information.
However, the amount of parameters that can be tuned is limited by how much data can be
measured in the experiment and by how such data can be incorporated into the model.
By increasing the number of sensors used, the model will be more accurate.
It is
important to keep in mind that if the model does not include information about a
particular sensor used, then the extra measurements will add no new information. For
example, in some of these experiments temperature measurements were taken at the feet.
However, since the model does not yet incorporate any information about temperature,
this information could not be used to tune any parameters.
53
8.2
Future Work
The system presented to estimate interstitial fluid in the legs is relatively simple. Many
assumptions have been made in order to simplify both the overall model of the system
and the sensors required to render valuable information. Under the situation specified,
the model is able to match the experimental setup well. However, the model currently
does not account for several other important factors that affect the signal.
The eventual goal is to be able to run the physical experiments and feed the information
directly into the complete Human Observer model. In order for this to be viable, more
data must be fed back into the model.
These data must be collected through added
sensors to the body. Heart rate monitoring sensors and especially temperature sensors are
essential in the next step of accuracy. Beyond these, there are other sensors that can also
be incorporated. Electro-myogram can measure the muscle activity of the legs and
determine whether there is muscl-related pumping of the venous blood by the muscles.
Continuous blood pressure would be also be a valuable parameter to have, however it is
still not practical to measure arterial blood pressure continuously and non-invasively.
The more parameters that are measured, the more complex the model must be in order to
integrate all the information relevant to the system.
54
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[20] Asada, H., Shaltis, P., Rhee, S., "Validation and Benchmarking of a High-Speed
Modulation Design For Oxygen Saturation Measurement Using Photo Plethysmographic
Ring Sensors," Progress Report 3-2, HAHC, 2001.
[21] www.fda.gov
[22] Barbagelata M, Asada H, Mori, T, Kitamura T, . "An Agent-Based Physiological
Digital Human and Its Application towards a Health Enhancing Chair" Progress Report
3-2, HAHC, 2001
[23] McCombie D, Asada H. "An Integrative Circulatory System Model Using
Foreground-Background Multi-Time Scale Simulation Environment" Progress Report 33, HAHC, 2002
[24] SchUtze H. Hildebrant W, Stegemann J. "The interstitial fluid content in working
muscle modifies the cardiovascular response to exercise." Eur J Appl Phyisiol (1991) 62:
332-336.
56
Appendix A
The following table shows each of the independent parameters used in the bicompartmental model. The table includes the parameter name used in the code, as well
as a description, the units and the initial values used. These initial values shall be
subsequently referred to as the base values
Table 7: Physiological Model
Name Units
--
Independent Parameters
Base Values
Description
PHYSICAL
rho
Kg/mA3
density of blood plasma
yh
yl
yu
meters
meters
meters
vertical height of the heart
vertical height of the lower body
vertical height of the upper body
1030.0
E
1.5
0.3
1.5
E
E
E
Aorta
Artery, Lower Body
Artery, Upper Body
Vena Cava
Vein, Lower Body
Vein, Upper Body
Interstitial fluid upper body
Interstitial fluid lower body
Right heat
9.OOE-09
5.OOE-10
5.OOE-10
2.75E-08
1.25E-08
1.25E-08
3.50E-05
6.50E-05
1.OOE-07
C
C
C
C
C
C
G
G
COMPLIANCES
Cal
Ca2
Ca3
Cv1
Cv2
Cv3
Cif2
Cif3
Cra
mA3/Pa
mA3/Pa
mA3/Pa
mA3/Pa
mA3/Pa
mA3/Pa
mA3/Pa
mA3/Pa
mA3/Pa
RESISTANCES
Rvl 1
Rvl2
Rvl3
Pa/(mA3/s)
Pa/(mA3/s)
Pa/(mA3/s)
vessel damping, vena cava
vessel damping, vein, lower
vessel damping, vein, upper
1.OOE+08
1.OOE+08
1.OOE+08
G
G
G
Ra102
Ral03
Pa/(mA3/s)
Pa/(mA3/s)
vessel resistance, arterial, lower
vessel resistance, arterial, upper
3.OOE+07
3.OOE+07
E
E
57
--
-
.1, I 'ill I-,-MAP
I-
1W.,
-
Rv102
Pa/(mA3/s)
-
-
-
- --.
vessel resistance, venous, lower
1.OOE+06
E
Base Values
Name Units
Description
Rv103
Pa/(mA3/s)
vessel resistance, venous, upper
1.OOE+06
E
Rart2
Rart3
Rbf2
Rlf2
Rbf3
Rlf3
Pa/(mA3/s)
Pa/(mA3/s)
Pa/(mA3/s)
lower body arteriole resistance
upper body arteriole resistance
Bulk Flow Resistance (lower body) capillary, interstitium
Bulk Flow Resistance (lower body) capillary, lymph capillary
Bulk Flow Resistance (upper body) capillary, interstitium
Bulk Flow Resistance (upper body) capillary, lymph capillary
1.44E+08
1.44E+08
2.00E+1 1
5.OOE+10
2.00E+1 1
5.00E+10
B
B
G
G
G
G
mA3
aortic volume
artery volume, lower
artery volume, upper
vena cava volume
vein volume, lower
vein volume, upper
interstitial volume, lower 6 Liters in cubic meters
interstitial volume, upper 4 Liters in cubic meters
Intial volume of the right atrium
9.60E-05
4.OOE-06
4.OOE-06
3.67E-06
3.33E-06
3.33E-06
3.50E-03
6.50E-03
0.OOE+00
E
E
E
E
E
E
E
E
E
bpm
ipm
ml
heart rate
respiration rate
stroke volume
75
20
70
E
E
E
molar concentration of protien in the blood
moles of protien in the lower body interstitial fluid
2.71 E+00
9.45E-04
B
B
moles of protien in the upper body interstitial fluid
1.76E-03
B
Pa/(mA3/s)
Pa/(mA3/s)
Pa/(mA3/s)
INITIAL VOLUMES
q10
mA3
q20
q30
q40
q50
q60
q70
q80
q90
mA3
mA3
mA3
mA3
mA3
mA3
mA3
OTHER
bpm
ipm
sv
BiComp -- Internal
Cb
mol/mA3
0.27
mol/mA3
0.27
mif2
mif3
mol/mA3
TCR
Pa/(mA3/s)
Total Capillary Resistance, 40% of avg. arteriole resistance
4.11E+07
B
R502
Pa/(mA3/s)
right heart valve resistance
1.OOE+07
G
B
E
C
G
-----
Physology Book: Human Physiology, Fluid dynamics
Estimated from known range
Calculated from estimated paramters (E, mu, L, r)
Guessed to fit the model
58
Appendix B
The table below shows the results from the sensitivity analysis.
The first column
contains all the independent parameters used in the bi-compartmental model, while the
first row contains extracted measurements from each of the relevant output parameters.
The larger the number, the larger effect a change in the independent parameter will have
on the output variable. The parameters that have the highest influence on each variable
are shown in bold and red numbers to help in their identification.
Table 8: Results from Sensitivity Study
Parameter
name
SV
Q2
jump
0.01
amount Qend Q2 beg Q2 end
sys
sys
changed sys
0.46
0.93
0.94
0.50
0.93
0.74
0.01
0.00
0.08
0.06
0.56
0.40
0.00
0.00
0.23
0.15
0.64
0.35
0.07
0.06
0.39
0.00
0.22
0.06
0.33
0.01
0.19
0.01
0.00
0.00
0.00
0.00
0.00
-0.01
-0.01
0.00
0.00
0.00
0.00
0.00
0.08
0.00
0.00
0.00
0.00
0.02
0.00
0.01
0.00
0.00
0.00
-0.10
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.20
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.17
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.20
0.00
0.00
0.00
0.00
0.00
0.00
-0.80
-0.32
-0.61
-0.21
0.00
-0.09
0.00
-0.07
0.00
-0.06
HR
-0.20
HR
-0.60
0.72
0.61
0.35
0.09
Rart2,Rart3
TCR
Ra102,Ra1O
1.00
1.00
1.00
0.44
0.12
0.10
0.50
0.14
-0.02
0.25
0.07
-0.01
Rv102,Rv 0
1.00
0.00
0.00
0.10
1.00
0.50
-0.40
0.20
0.20
0.50
0.50
1.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1
3
Rbif2
Cb
Rbif2
leg ht.
q80
q70
q80
q70
q80
q70
Q7
slope
0.21
0.44
0.36
0.10
0.60
3
05
jump
0.00
0.90
0.73
SV
HR
-762
Q5 end Q5 beg
sys
sys
0.59
0.09
59
.. - -
7-
q20
q1O
Parameter
name
-
- -
......
......
- -- -
-
0.00
0.00
0.00
0.20
0.00
0.13
0.00
0.50
end
Q2
beg
Q2
amount Olend
sys
sys
changed sys
0.00
-0.12
Q2
jump
-
- 1 . .................
..............
-
0.00
0.00
0.06
0.00
05 end Q5 beg
sys
sys
0.00
-0.01
05
jump
0.00
0.00
07
slope
q40
q60
q4
q30
q4
q30
q30
qlO
q60
q1
q
q20
q20
q60
q50
q50
C: if
RbI
mIf2,mIf3
Rblf3
rho
0.20
0.20
0.50
0.50
1.00
0.20
1.00
0.20
1.00
1.00
1.00
1.00
0.50
0.50
0.50
0.20
1.00
0.50
1.00
0.10
2.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.14
0.00
0.15
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.51
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.14
0.00
-0.14
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.85
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.02
0.00
0.11
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.12
0.04
1.00
heart,upper
ht
-0.20
0.00
0.00
0.61
1.20
1.03
0.00
1.20
1.18
heart height
-0.20
0.00
0.00
0.61
1.20
1.03
0.00
1.20
1.17
0.00
0.99
0.91
1.01
0.00
0.00
0.00
0.00
0.01
-0.01
0.00
0.01
0.00
0.00
0.00
0.00
-0.01
0.00
1.00
-0.01
-0.02
-0.01
-0.03
-0.09
0.01
0.92
0.00
0.00
0.00
0.00
0.00
0.00
1.01
0.11
0.00
0.00
0.00
-0.02
0.00
0.00
C: v
1.00
0.00
-0.01
0.00
ml2,mif3
Ipm
Cra
ipm
Cra
C: a
C: a & v
1.00
0.50
9.00
-0.50
1.00
1.00
1.00
0.00
0.00
0.00
-0.01
-0.01
-0.09
-0.09
0.00
0.00
0.00
-0.01
-0.01
-0.09
-0.10
0.00
0.00
0.00
0.00
-0.01
-0.04
-0.05
The second column of the table above shows the amount by which the independent
variable has been changed.
This value is necessary to normalize the sensitivity for
different parameter changes. The following example will show how the information was
acquired for the shaded box.
60
First the independent parameter disturbed is the heart rate which was changed from a
base value of 75 bpm to 60 bpm. This resulted in a change of -0.20 as shown in the
second colunm. The systolic value for the aortic pressure was extracted both before the
change in heart rate and after.
calculated
P
-P
aft"e'
befo"
Then the effect of the change on the pressure was
. Finally the pressure change effect is divided by the effect of the
before
parameter change
AEffectpressue
and a normalized value is acquired.
AEffectheart rate
61
..........
Appendix C
The following table shows the values for the tuned independent parameters as compared
to the original base parameters.
These parameters simulate the responses shown in
Chapter 6. The values in red bold numbers shown which parameters have been changed
through the tuning procedure.
Table 9: Tune independent parameters
Base Tuned
Name IDescription
PHYSICAL
rho
density of blood plasma
yh
yl
yu
vertical height of the heart
vertical height of the lower body
vertical height of the upper body
1030.0
1057.0
1.5
0.3
1.5
0.85
0.25
0.85
9.OOE-09
9.OOE-09
5.OOE-10
5.00E-10
2.75E-08
1.25E-08
1.25E-08
3.50E-05
6.50E-05
1.00E-07
5.OOE-10
5.OOE-10
2.75E-08
6.25E-09
6.25E-09
3.50E-05
6.50E-05
0.00E+00
COMPLIANCES
Cal
Aorta
Ca2
Ca3
Cvi
Cv2
Cv3
Cif2
Cif3
Cra
Artery, Lower Body
Artery, Upper Body
Vena Cava
Vein, Lower Body
Vein, Upper Body
Interstitial fluid upper body
Interstitial fluid lower body
Right heat
RESISTANCES
Rvl1
Rvl2
Rvl3
vessel damping, vena cava
vessel damping, vein, lower
vessel damping, vein, upper
1.OOE+08
1.OOE+08
1.00E+08
1.OOE+08
1.OOE+08
1.OOE+08
RalO2
Ral03
Rv102
vessel resistance, arterial, lower
vessel resistance, arterial, upper
vessel resistance, venous, lower
3.OOE+07
3.OOE+07
1.00E+06
3.00E+07
3.OOE+07
1.OOE+06
62
Rv103
1.00E+06
vessel resistance, venous, upper
Base Tuned
Name Description
Rart2
Rart3
Rbf2
Rlf2
Rbf3
Rlf3
1.00E+06
lower body arteriole resistance
upper body arteriole resistance
Bulk Flow Resistance (lower body) capillary, interstitium
Bulk Flow Resistance (lower body) capillary, lymph capillary
Bulk Flow Resistance (upper body) capillary, interstitium
Bulk Flow Resistance (upper body) capillary, lymph capillary
1.44E+08
1.44E+08
2.00E+1 I
5.00E+10
2.00E+1 I
5.00E+10
O.OOE+00
O.OOE+00
4.00E+1 I
5.OOE+10
2.00E+1 1
5.OOE+10
9.60E-05
4.00E-06
4.OOE-06
3.67E-06
3.33E-06
3.33E-06
3.50E-03
6.50E-03
O.OOE+0O
0.00E+00
7.20E-05
4.OOE-06
6.66E-08
7.33E-06
1.67E-06
3.50E-03
6.50E-03
0.OOE+00
75
20
70
68
20
70
INITIAL VOLUMES
q10
q20
q30
q40
q50
q60
q70
q80
q90
aortic volume
artery volume, lower
artery volume, upper
vena cava volume
vein volume, lower
vein volume, upper
interstitial volume, lower 6 Liters in cubic meters
interstitial volume, upper 4 Liters in cubic meters
Intial volume of the right atrium
OTHER
bpm
ipm
sv
heart rate
respiration rate
stroke volume
BiComp - Internal
Cb
mif2
mif3
molar concentration of protien in the blood
moles of protien in the lower body interstitial fluid
moles of protien in the upper body interstitial fluid
2.71 E+00
9.45E-04
1.76E-03
2.71 E+00
9.45E-04
1.76E-03
TCR
Total Capillary Resistance, 40% of avg. arteriole resistance
4.11 E+07
4.11 E+07
R502
right heart valve resistance
1.00E+07
1.001E+07
63