A Dynamic Simulator for the Management of Disorders of
the Body Water Metabolism
Ozge Karanfil
Graduate Student, Centre for Nonlinear Dynamics
Department of Physiology '
McGill University
Montreal, Quebec, Canada
Telephone: +1 (514) 952-7882
E-mail: ozge.karanfil@mail.mcgill.ca
ABBREVIATIONS
ADH, Antidiuretic Hormone; ALD, Aldosterone; ANG, Angiotensin; ANH, Atrial
Natriuretic Hormone; BV, Blood volume; DI, Diabetes Insipidus; EC,
Extracellular; ECFV, Extracellular fluid volume; ECNa, Extracellular sodium; ECOsm,
Extracellular osmolality; GFR, Glomerular Filtration Rate; IC, Intracellular; ICFV,
Intracellular fluid volume; ICOsm, Intracellular osmolality; K, Potassium; L, Liter;
MAP, Mean Arterial Pressure; Na, Sodium; PV, Plasma volume; RAAS, Renin-
Angiotensin-Aldosterone System; SIADH, Syndrome of Inappropriate Antidiuretic
Hormone Secretion; TBW, Total body water; U, Urine (or Urinary); UNa, Urinary
sodium; UOsm, Urine osmolality; V, Volume; mEq, milliequivalents.
ABSTRACT
In this study, a simulation model is built to study the body water regulation and its
disorders by focusing on the fundamental feedback mechanisms in the normal and
disease physiology. This model is then extended to include related therapeutic
interventions of the most common body fluid disorder, namely water intoxication/
hyponatremia, and a game version is produced to test the possible effects of a given set
of treatment options on a simulated patient. The model is shown to adequately
reproduce the changes in the body fluid balance in normal and diseased states. The
interactive simulation game version of the model proves to be a useful experimental
platform to describe changes that are known to occur after administration of various
pharmacological means. Game results demonstrate that hypertonic saline should be
given carefully concurrently with drugs that increase urine flow. The model and the
game version constitute an experimental laboratory for a closed-loop therapy approach
to hyponatremia.
1. INTRODUCTION
The homeostatic regulation of body fluids is important in almost every field of
medicine and has been thoroughly investigated in this century. In health, total body
water and its distribution throughout the body is maintained between narrow limits. This
' Research done while at Bogazici University, Department of Industrial Engineering, Istanbul-Turkey:
Supported by Bogazici University Research Grant no. 02R102
task is accomplished by two distinct but interactive systems that respectively regulate
the extracellular sodium concentration/body water and the blood volume/sodium
content.
The main feedback system for body water regulation is the Antidiuretic Hormone
(ADH)-thirst system, and the main feedback mechanisms for sodium balance include
the Aldosterone (ALD) and the Atrial Natriuretic Hormones (ANH), and the renal
mechanisms. In ADH-induced hyponatremia, both the ADH and the thirst feedback
loops are dysregulated, and the result is a lower sodium concentration and higher body
water content, which may cause serious consequences.
Problems associated with body fluid disorders are very common in hospitalized
patients. Among these, water intoxication (or hyponatremia) defined as an abnormally
low level of EC sodium concentration, is the most important body fluid disorder with
the potential for significant mortality. The treatment of hyponatremia constitutes a
problem, partly because all available therapies have significant limitations. Furthermore,
it is observed that a big portion of hyponatremia incidences are in fact “hospital-
acquired”. Most of these patients acquire hyponatremia as they receive intravenous
fluids, which is a very common practice in hospitals. Today, more than 75% of
currently recommended intravenous fluids are in the form of electrolyte-free water,
which is known to aggravate hyponatremia (Halperin and Bohn, 2002). This growing
trend raised doubts related to hyponatremia, and inspired many studies on its diagnosis
and optimum therapy (Shafiee et al., 2003).
Due to the feedback complexity of the underlying structure and its interactions with
various pharmacological means, body water regulation and its disorders constitute a
suitable area for system dynamics simulation modeling. However, no closed-loop
therapy approach for disorders of dysnatremias has been yet attempted (Northrop,
2000). This study attempts to build a closed-loop system dynamics model for body
water disorders, and particularly for ADH induced hyponatremia.
2. CLINICAL ABNORMALITIES OF BODY FLUID REGULATION
Any influence which alters the balance of the body water or sodium metabolism
inevitably affects the balance of the other. Therefore, it is important to differentiate the
clinical abnormalities of ECF volume/Na content from those of the TBW/osmolality
regulation.
2.1 Disturbances of Body Sodium C ontent
As the major cation of the EC fluid, the sodium content determines the ECFV.
Therefore disorders of sodium metabolism are always manifested as disorders of
volume status. Moreover, due to the close interrelationship between ECFV and the
mean arterial pressure (MAP), MAP is also dysregulated. Disorders of sodium
metabolism commonly coexist with disorders of water and fluid-electrolyte balance.
2.2 Disturbances of Water Metabolism: Dysnatremias
Disorders of water metabolism are clinically manifested by disorders of EC sodium
concentration (dysnatremias), since the regulatory systems controlling water
metabolism do so by maintaining a constant EC sodium concentration. Loss of water
leads to hypernatremia and widespread functional disturbances in the brain. On the
other hand, accumulation of water leads to hyponatremia, cell swelling and disturbances
in central nervous system.
In general, failure to maintain body water between narrow limits includes two
components. The first one is associated with the capability to dilute or concentrate urine
appropriately, and the second one is associated with the thirst function. If one of these
components fails to function properly, the other component may still compensate this
failure. (Jamison et al., 1982).
Hyponatremia is the most common and potentially serious electrolyte abnormality
in hospitalized patients (Shafiee et al., 2003). It is defined as an EC sodium
concentration of less than 135 mEq/L. The most common causes of hyponatremia are
the Syndrome of Inappropriate Antidiuretic Hormone Secretion (SIADH) (38%),
incorrect hydration (19%), and continuous diuretic treatment (30%) (Halperin and
Bohn, 2002).
3. DYNAMIC MODELING OF PHYSIOLOGICAL SYSTEMS
3.1. Systems Theory in Physiological Models
Hippocrates held the idea that disease is cured by natural powers, but the
corresponding term of “homeostasis” was first used far later by Walter Cannon, in his
book The Wisdom of the Body (1932). Cannon made a qualitative use of the concepts of
today’s dynamic systems and suggested that physiological systems are dominated by
negative feedback loops. The second pioneer of systems thinking in physiology, namely
Arthur Guyton, was the first to introduce the concept of systems analysis to physicians,
whose approach then led to the emergence of biomedical engineering.
3.2. Models for Fluid-Electrolyte Dynamics
The system for regulation of body fluid volume is important to understand diseases
such as hypertension and dysnatremias. First models that represent certain aspects of
renal control of body fluids belong to DeHaven and Shapiro (1967) and Reeve and
Kulhanek (1967). Integrated models of body fluid regulation that also consider the
circulatory system include those by Ikeda (1979) and Abbrecht (1980). However the
most complex analysis of body fluid dynamics belongs to Guyton and co-workers, who
constructed an overall circulatory model for examining the causes of hypertension. This
model has inspired many other studies in this field, e.g. Cameron (1977), Badke (1972),
and Uttamsingh (1981). Uttamsingh (1985) also extended his model for the clinical
application of patients with renal failure. Recently, a long-term cardiovascular system
model is developed by Karaaslan (2004) that integrates the previous models developed
by Guyton, Uttamsingh and Coleman.
4, DESCRIPTION OF THE MODEL
The purpose of this modeling study is to develop a dynamic representation of our
body fluid balance in normal and diseased states. For this purpose, this modeling study is
divided into three parts. In the first part, the normal physiology of the body water balance
and its stability will be clarified, and in the second part, the dynamics hyponatremia will
be investigated. Lastly, the modified model of the second part will be used in an
interactive simulation game for exploring the possible effects of therapeutic
interventions, and finding a successful therapy.
Two major systems that are involved in the homeostatic regulation of body fluids are
the system that regulates the osmolality/body water and the system that regulates the
blood volume/sodium content. In this study, the central controller is the hypothalamus,
and thus the normal values of all the regulated variables are taken as exogenous
constants, e.g. the set point for ADH and the set point for blood volume. The effector
organ of the body fluid system is the kidney.
The model is composed of nine sectors grouped under five sector groups. These
sector groups correspond to body water, sodium, hormonal system, urinary sodium
concentration, and treatment. In addition to these five sector groups, there are other
structures in the model, which do not belong to any of these sectors but are used for the
game, messages, extra measurements, time tracing converters, etc.
The initial states and parameters are standard values which are quoted frequently in
the major medical textbooks and in earlier models. When available, published
experimental data is also used. The model assumes a standard healthy human male of
approximately 70 kg with 40 liters of body water.
4.1. Control of Total Body Water and Osmolality
The mechanism for the regulation of water balance is often referred to as the ‘thirst-
ADH mechanism’. The two most important factors that are monitored by this mechanism
are EC osmolality and intravascular volume (blood volume). EC osmolality represents
the number of particles in a given mass of water, usually expressed as millimoles (or
milliequivalents) per kilogram of water.
Under usual conditions, control of EC osmolality means almost the same thing as
controlling the ECNa concentration, since ECNa is the substance that mostly
contributes to the EC osmolality. Its importance in terms of water balance is that control
of EC osmolality controls IC volume. Three facts about the body water and body
sodium verify this argument: First, sodium is mostly restricted to the EC fluid; second,
intracellular solute does not change easily, third, EC osmolality must equal IC
osmolality. It should be noted that the mechanisms that control the ECNa
“concentration” and the ECNa “amount” are different, albeit interacting. ECNa
concentration has a normal value of 142 mEq/L, and is found by division of EC sodium
content (ECNa) by ECFV.
Figure 4.1 provides a causal-loop diagram of the body water/osmolality control
system. The Ist and the 2nd loops demonstrate the ADH-thirst feedback mechanism for
EC osmolality and body water control. Increasing EC osmolality increases the level of
ADH, and as a consequence of increased urinary concentration, water excreted in urine
decreases. At the same time, thirst perception is stimulated and water intake is increased.
It is assumed that stimuli acting on ADH secretion do so as an additive sum and the
response of ADH takes effect immediately.
extracellular a
volume (ECFV)
extracellular sodiun (2-f
concentration eS
* drinking
“
‘a + blood
1- volume/pressure
€ Antidiuretic Total Body Water
‘tered sodium | Hom™one (ADE) (rBW) 43)
load }
+™ urine sodium
concentration, +
glomerular filtration
sodium excreted rate (GFR)
in urine
Figure 4.1. Causal-loop diagram for body water/osmolality control
Drinking is considered as the only source of fluid intake. Both continuous and
discontinuous drinking options are modeled to simulate the drinking behavior. The
model developed by Reeve and Kulhanek (1967) forms the basis regarding the drinking
structure in this study. Accordingly, discontinous drinking is considered as a constant or
variable rate mechanism governed by on-off switches and inhibitory feedback. For the
continuous drinking structure, drinking rate is is defined as a function of EC osmolality
(See Figure 4.2).
ro00
eof
ECDem cn
inking
jaz
m0 JT + [ooo ma [> fom
(A) Fo T T Tiooo
Figure 4.2. Effect of ECOsm on drinking
A constant water loss, which represents the continuous escape in the form of
evaporation, and a varying urinary loss represent the two sources of loss of water from
the body. The urine flow rate is determined by two variables, i.e. the urinary sodium
concentration (UNa_conc), and the rate of sodium excretion (na_out_in_urine). The
underlying assumptions are: 1-The rate of water transport is always proportional to the
rate of solute transport, 2-The urine flow is inversely related to the urinary concentration
assuming a given sodium outflow (Bray et al., 1989). Ordinarily the urine flow
rate*urine osmolality (which equals to the amount of solute excreted) is relatively
constant. The equation of the implied_UFlow is:
implied _UFlow= na_out_in_urine
~ UNa_ conc x1000
Under normal physiological conditions, the ADH level is the main determinant of
urine osmolality. The upper limit to the maximal concentration of urine is about three-
four times the osmolality of plasma (Janicic and Verbalis, 2003). Accordingly, the effect
of ADH on UNa_conc is formulated with a graphical function (See Figure 4.3). The UNa
concentration implied by ADH (implied_UNa_conc_by_ADH) is formulated by dividing
the normal UNa concentration by the effect of ADH:
normal UNa_conc
implied UNa_conc_by_ ADH = eff of ADH
200
off of ADH
ooo
[ra I ica Daw
Tow T i Fond)
DH satin ta nowmal
Figure 4.3.Effect of ADH on UNa concentration
However, there are other factors that can regulate urine osmolality and dilution in
the absence or excess of ADH, i.e. the GFR. In addition to that, the effects of some drugs
on urinary concentrating/diluting capacity of the kidney are also presented in the
modified Game version of the model.
Other mechanisms that can influence the urine flow rate/urinary concentration are
the Glomerular Filtration Rate (GFR) and the sodium excretion rate. GFR represents the
amount of filtrate formed per minute and so it determines the amount filtered for any
substance in the kidney. An increase in GFR increases urine flow via a decreased rinary
concentration (3rd loop). As seen in the diagram, GFR and the EC sodium concentration
influence the sodium excretion rate by changing the filtered sodium load (4th and Sth
loops).
4.2. Control of Total Body Sodium and Extracellular Fluid Volume
Total body Nat is restricted mostly to the ECF. Hence day to day variations in the
amount of body Na+ represent variations in ECF volume (Bray et al., 1989). Since the
EC and the IC osmolalities are always identical, and IC solute is assumed to be
constant, the EC fluid volume (ECFV) is calculated as follows:
ECFV =TBW xECNa_ratio_to_total/1000
ECNa
ECNa_ratio_to_ total =————___
= Se (ECNa+IK)
In modern societies the sodium intake is always greater than necessary for
homeostasis. Therefore, sodium intake rate is assumed to be constant in the model.
According to the most recent knowledge, sodium excretion mainly involves three
factors: the filtered load, ALD, and ANH.
Figure 4.4 provides a brief causal-loop diagram that demonstrates the causal
mechanisms related to these three factors. The Ist and the 3rd loops are related to
balancing effects of the filtered load. Filtered load refers to the rate at which substances
are filtered in the kidney. It is found by the equation: GFR = plasma concentration of the
substance (Guyton, 2000). Any change that causes an increase in the filtered load of
sodium causes a rise in sodium excretion. On the other hand, the 2nd loop indicates that
an increase in ECNa also has a decreasing effect on ECNa concentration due to the fluid
shift between the IC and the EC compartments. The remaining balancing loops relate to
the effects of the ANH and ALD hormones. The response of ANH is assumed to take
effect immediately, however ALD responds to the value of stimuli after a delay.
Therefore, ALD is important for long-term adjustments of sodium excretion (Bray et al.,
1989), whereas ANH (together with changes in filtered load) is responsible for short
term adjustments.
The sodium excretion rate (na_out_in_urine) is formulated as as a multiplicative
effect formulation:
na_out_in_urine=Filtered_Naxnormal_ fractx
eff of ANH _on_na_excrxeff of ALD _on_na_excr
G) extracellular Ou
ns volume (ECFV)
ECNa ratio‘to
total 424)
.
a * . blood
f
ae ECNa cone. volume/pressure
Natriuretic
Hormone
(ANH)
Bow
ep Extracellular
Sodium (ECNa)
+
eff of ANF
\)v
na out ou /
glomerukr filtration
rate (GFR)
Renin
Seu ALD [Aldosterone]
(ALD)
af
Figure 4.4. Simplified causal-loop diagram for sodium and ECFV regulation
4.3, Integrated Body Water and Sodium Regulation
Figure 4.5 gives an overall appreciation of how the two control systems of body
water and body sodium integrate to produce a tight control system. This diagram may
also help to differentiate the clinical abnormalities of EC fluid volume/Na content
regulation from abnormalities of body water/osmolality.
In SIADH, the degree of water retention is limited due to the adaptive mechanisms
of the body, i.e. the kidney adapts via a transient natriuresis and a persistent diuresis. In
fact, the pathophysiology of this disease can be better understood when the causal-loop
diagram presented below is examined carefully.
Main features of the SIADH are drastically decreased EC sodium concentration, a
clinically normal ECFV, normal/mildly elevated blood pressure and an increased GFR. It
is seen that the EC/blood volume regulation is appropriate; however the osmolality/TBW
regulation is deranged. As the TBW increases due to increased ADH levels, both EC and
the IC volumes increase. However a transient natriuresis induced by the ANH and ALD
hormones acts to defend the EC volume and protects the body from a hypertensive state.
Therefore, most of the excess fluid is accumulated in the IC fluid. However, to achieve a
steady-state condition, fluid intake and output must be precisely balanced. Thus, a mild
elevation in GFR can be considered as an adaptive response of the body to compensate
the high urinary concentration induced by ADH.
Le
* extracellular fluid
ECNa i to volume CG V)
total
intracellular fuid
‘ L4¥- volume (ICFV)
zwul lM ECNa cone + i
Natriuretic baa
Hormone
(ANH) \
'
i
Total Body
. ‘Antidiuretic Water (TBW) ‘mean arterial
Homone pressure (MAP)
Bxtracclular (ADH) - .
Sodium
frat ; a
PM UNa conc.
urine flow (UFlow)
‘OM na load 2
ita out in urine Ch
glomerular filtration
rate (GFR)
aldosterone
(ALD)
Figure 4.5. Overall regulation of body fluids by integrated control of body water
and body sodium regulators
5. VALIDATION AND ANALYSIS OF THE MODEL
A formal validation process is followed in order to detect structural flaws of the
model (Barlas, 1996) which is integrated to the model building process. Many direct
structure tests are performed during the model building, which are not presented here.
The validation of the model is basically demonstrated by performing “structure-oriented
behavior tests” proposed in literature, such as extreme condition and behavior
sensitivity tests, and a selected sample is presented. The model behavior is also
compared with the real data, where data are available.
5.1. Basis Dynamics of the Model
5.1.1. Base Behavior of the Model
The continuous version of the model shows a steady state behavior when all its
levels are initialized at their equilibrium values, and the discontinuous drinking version
of the model demonstrates the normal daily variations in the key variables (See Figures
5.1 and 5.2). It can be seen that the ECNa and the MAP show almost no change during
the day. The main change can be seen in the dynamics of the urine flow, drinking, and
the UNa concentration, since water is continuously lost and then replenished by
drinking. As a result, the TBW is maintained within the normal limits.
Tew 2: ECNa 3: ECNa cone 4: MAP
0.00 6.00 12.00 18.00 24.00}
Untitled
Figure 5.1 . Equilibria of the key variables with discontinuous drinking
lurine flow 2: UNa conc 3: drinking
LZ lV sl
0.00 6.00 12.00 18.00 24.00
Hours
Untitled
Figure 5.2. Equilibria of the key variables with discontinuous drinking-2
5.1.2. Water Loading
The dynamics of body fluids after water loading constitutes one of the fundamental
tests of the interaction between body fluids and the kidney. For this simulation, the
normal_drinking variable is set to 0, and a pulse of water input of 1000 ml is given at
time 0. The urine flow rate increases about 11 fold in one hour, and after 3 hours it
returns to its normal value (See Figure 5.3 and 5.4).
10
;, & 7
© 12 = 1500 12
a
c ob & Mt & s000 it ge °
8 * ¢ 8
z . 4 } 3 : °
© 4 5 © 500} =4 ®
‘ . A rm oF Ble
5 fee | : ty 5
P ee 1 5 ia ares} er) LAr cs n
g$ “0 t 2 3 o 1 2 3 o 1 2 3
Z time, h time, h time,
Figure 5.3. Urine flow following ingestion of 1 L of water;(a) data from Baldes and
Smirk, 1934, (b) data for eight subjects, (c) data for one subject - (Uttamsingh, 1985)
urine flow rate. mi\min 2: na excr ratio
12.0:
5.0
i
0.00 1.00 2.00 3.00 4,00
Hours
Untitled
Figure 5.4. Base dynamics of urinary excretion following ingestion of | L of water
Figure 5.5 gives a schematic representation of the normal physiologic relationships
among ECOsm, ADH concentrations, UOsm, and urine volume. Accordingly, urine
osmolality is proportional to plasma ADH levels, but urine volume is inversely related to
urine osmolality.
11
Figure 5.5 Normal physiologic relationships among EC osmolality, ADH
concentration, urine osmolality, and urine volume in man (from Verbalis, 2003)
The model simulated results for the relationship between the urine flow and the
UNa concentration in the base run and the water loading tests are given in Figure 5.6.
“OSMOLALITY
THIRST
osmoTic
THRESHOLD
AVP.
OSMOTIC —>
THRESHOLD
a
(mOsmikg H,0) (ogi)
10.
9
URINE
OSMOLALITY
(mOsm/kg H,0)
o 4
8 12
URINE VOLUME
(Uday)
16 20 24
3009
1504
UNa conc v. urine flow : 1 -
200%
1004
UNa conc v. urine flow : 1-
‘t, | eae,
French oe
0
0 200 400 0 375 750
urine flow urine flow
Untitled Untitled
Figure 5.6. Simulated relationships among urine flow and UNa concentration (a)
for the base run, (b) after ingestion of 1 L of water
12
5.2. Experiments with C hanges in Daily Water Intake
This set of experiments is simulated by varying the daily water intake
(normal_drinking) of the person from its normal value, which is about 2,2 liters, and
resetting the thirst feedback on drinking. The main effect of an elevated (decreased)
water intake is a great fall (rise) in the UNa concentration and a consequent rise (fall) in
the urine flow. There is almost no change in the TBW, MAP, and the ECNa, as long as
the fluid intake and the fluid loss are precisely balanced. A representative dynamic of
the key variables is given in Figure 5.7.
ECNa 2: ECNa cone 3: MAP 4: TRW
2130.00:
2120.00
141.50,
101
40150
2110.00
140.50
100
40000:
0.00 14.40 28.80 43.20 57.60 72.00
Hours
Untitled
Figure 5.7. Dynamics of key variables in case of increased daily water intake
Sensitivity of Blood Volume to Different Levels of Daily Water Intake: Under normal
conditions, blood volume is not affected by changes in fluid intake (Guyton, 2000).
Figure 5.8 demonstrates the fact that the blood volume remains almost constant despite
extreme changes in fluid intake. The simulated results are in accordance with the real
case.
6
Blood volume so.
5
Normal range sor 4
4 5002 4
=o 4332 |
3B 2 4967
a
4.982
1
4977 ——_—_——eeoarr
: > A % & A
T T 5 T T LR T T
o 1 2 3 4 5 6 7 4 Daily Water Intake
Daily fluid intake (water and electrolytes) (L/day)
Figure 5.8 a) Approximate and b) simulated effect of changes in daily fluid intake
on blood volume (b) from Guyton, 2000
13
5.3. Experiments with C hanges in Daily Sodium Intake
This set of experiments is simulated by varying the daily sodium intake of the
person from its normal value. The results demonstrate that changes in sodium intake
have little effect on the ECNa concentration and the TBW, but they have a great effect
on the ECFV, BV, and MAP. A representative dynamics of the key variables is given in
Figures 5.9 and 5.10.
ECNa 2: MAP. 3: ECNa conc 4: TRW
2300.00:
115
146.0
40250
2200.00
105,
144.0
40100
2100.00
95
142.0
399504 - 7
0.00 7.20 14.40 21.60 28.80 36.00|
Hours
Untitled
Figure 5.9. Dynamics of key variables in case of 4-fold increased sodium intake
lwater lost 2: drinking 3: urine flow 4: na out in urine 5: UNa cone
0.00 9.00 18,00 27.00 36.00
Hours
Untitled
Figure 5.10. Dynamics of key variables in case of 4-fold increased sodium intake-2
Sensitivity of ECNa_concentration to Different Daily Sodium Intakes: In a normal
person, ECNa concentration is controlled with reasonable effectiveness even with large
changes in sodium intake, as long as water intake is enough to balance the losses
(Guyton, 2000). In this experiment, the effectiveness of body feedback mechanisms to
control the ECNa concentration is investigated. The system is initialized with all
variables being at their normal levels, and sodium intake is varied between 0.2 of normal
salt intake and 5 times normal intake, a range of 25-fold. It is seen that ECNa
14
concentration is kept within 1% control limits when all feedback systems are intact (See
Figure 5.11 and Table 5.1).
ECNaconc:1-2-3-4-5-9 7
1 146.50
1 143.50
1 140.505} 1
0.00 18.00 36.00 54.00 72.00
‘age 2 Hours
N Untitled
Figure 5.11. Sensitivity of ECNa concentration to different daily sodium intakes
Table 5.1: Simulated levels of ECNa concentration with different daily sodium intakes
Runs] Dietary Sodium (times normal) | ECNa concentration
1 0.2 140.63
2 0.50 141.11
3 0.8 141.5
4 1 142
5 2 143.27
6 3 144.23
7 5: 145.66
In the second experiment, the effect of ADH-thirst feedback system on ECNa
concentration is investigated. The experiment is repeated by blocking the ADH and then
the thirst systems, and it is seen that each one of the ADH and the thirst systems can
control the ECNa concentration on their own with reasonable effectiveness. On the other
hand, if both of them are blocked simultaneously, ECNa concentration changes
tremendously, as expected (See Figure 5.12 and 5.13).
15
ADH and thirst”
a systems '
oa blocked Ps
- . - © 7
0 660) 8D D120 «150 180)
Sodium mlake {mEqiday}
Figure 5.12. Effect of changes in sodium intake on ECNa concentration (1) under
normal conditions (2) after the ADH-thirst feedback has been blocked -from Guyton
(2000).
200
190
180 7
170 «
160 2
150 o
140 ca —»— ADH-thirst
ea blocked
-
130 nai
120 =—=
110
100
Normal
0.2 04 06 08 1 13 16 19 23
sodium intake (times normal)
Figure 5.13. Simulated effect of changes in sodium intake on ECNa concentration
(1) under normal conditions (2) after the ADH-thirst feedback has been blocked
In the third experiment, the effect of ALD feedback on ECNa concentration is
sought, so the experiment is repeated by blocking the ALD feedback (See Figure 5.14
and 5.15). It is seen that ECNa concentration is almost equally well controlled with or
without ALD feedback control, which demonstrates that the ECNa concentration is
mainly controlled by the ADH-thirst system, and ALD has little effect on the ECNa
concentration.
16
Plasma sodium concentration
100+ r r
Aldosterone system blocked
0 30 6 90 120
150
Sodium intake (mEq/L)
180 «21
Figure 5.14. Effect of changes in sodium intake on ECNa concentration (1) under
normal conditions (2) after the ALD feedback has been blocked-from Guyton (2000)
150
148
146
144
—
140 +=
Normal
138
136
—— ALD
blocked)
134
132
130
0.3
0.5 0.8 1 12 615 2
Sodium intake (times normal)
2.5
3
Figure 5.15. Simulated effect of changes in sodium intake on ECNa concentration
(1) under normal conditions (2) after the ALD feedback has been blocked
6. THE INTERACTIVE DYNAMIC SIMULATOR (BWATERGAME)
6.1. Modification of the Model
First, some sectors or structures are added to the original model for representing the
treatment options, and the variables for game related measurements. Second, some
equations and graphical functions of the original model are modified to incorporate the
effects of treatment options and of a disease process.
17
6.1.1. Structures A dded to the Original Model
The treatment sector is composed of three sub-sectors, from which two of them are
almost identical, i.e., Diuretic and Aquaretic (or ADH-Antagonist) sectors. These sectors
represent the most commonly used drugs for treatment of hyponatremia. The drug
metabolization structure used in New Horizons in Virtual Medicine- A Simple Model of
Drug Metabolization of High Performance Systems, Inc. (1997) (See http://www.hps-
inc.com/community/downloads/EducationDownloads.aspx) is evaluated to be
appropriate for the scope of this study. The third subsector, i.e., intravenous fluid
infusion constitutes another important part of the current standard therapy for treating
severe hyponatremia. The three most commonly used categories are presented in the
model, namely hypertonic, isotonic, and hypotonic fluids, which are classified according
to their sodium content.
Other structures that are added to the game are related to the measurements of the
game variables, finding the hourly and daily EC sodium concentration correction rates,
time tracing converters, and initialization variables.
6.1.2. Modified Structures of the Original Model
Both thirst function and ADH have to be dysregulated to bring about hypoosmolality
in the SIADH. Therefore, first the set-level of the ADH concentration is increased, and
then the thirst function of the potential patient is modified. Accordingly, the patient has
an elevated normal fluid intake and she cannot sufficiently suppress her water intake by
hypoosmolality. The equations for the UNa concentration are also modified to include
the effects of a possible administration of the Aquaretic and the Diuretic drugs.
The equation for drinking is modified since a mild or severe water restriction can be
imposed on the patient as a treatment option. The modified drinking equation is:
Drinking=unrestricted_intake*(unrestricted_drinking)+mild_water_restriction* (IF(mild/24)<(u
nrestricted_drinking)THEN(mild/24)ELSE(unrestricted_drinking))+severe_water_restriction*((
IF(severe/24)<(unrestricted_drinking)THEN(severe/24)ELSE(unrestricted_drinking)))
6.1.3. Validation and Analysis of the Modified Model
To verify the new drug sectors of the modified model, they are first simulated in
isolation, and then a series of experiments are done to test the validity of the treatment
options. Yamamura et al. (1993) investigated the responses to a series of intravenous
doses of Aquaretics in a group of healthy, normally hydrated men. The real cumulative
urine volume and the model behavior are presented in Figures 6.1 and 6.2.
18
2000
1500
Cumulative Urine Volume
(m))
3
8
500
Time
(h)
Figure 6.1. Cumulative volume-time relationship of a series of doses of Aquaretic
in comparison to placebo (dotted lines) (Modified from Yamamura et al., 1993)
mulative Urine Volume: 1-2-3-4-5-
2000:
1000:
0.00 6.00 12:00 18:00 24.00
Hours
Untitled
Figure 6.2. Model behavior
The modified model is then used to demonstrate the appearance of hyponatremia in
the SIADH. To develop hyponatremia, both ADH and the thirst function have to be
dysregulated. This fact is demonstrated by simulating the modified model 1°, by
increasing the ADH level without changing the thirst function, and a by disturbing the
thirst function without changing the ADH function. It is seen that the resulting decrease
in ECNa_conc is very small.
However when both ADH and the thirst function are dysregulated, there is no
mechanism that can preserve the level of the body water and the ECNa_conc. An
example dynamic for the appearance of hyponatremia are given in Fig 6.3. In five days,
the ECNa_conc of the patient falls to 120 mEq/L, and the TBW is increased by about 5
liters. The final values of this simulation are used for the initialization of the game.
19
Tew 2: ECNa 3: ECNa conc 4: ECFV 5: MAP
45000:
2200
145.0
15
Sea
103 : i
ie —
0.00 24.00 48.00 72.00 96.00 120.00
Hours
Untitled
i \\
Figure 6.3. Appearance of hyponatremia when both ADH and the thirst functions
are dysregulated
6.3. Game Description
The player plays the part of a physician, who is trying to treat a hyponatremic
patient by seeking a delicate balance among weighing the risks of hyponatremia itself
and those associated with rapid correction of hyponatremia. The patient has an ECNa
conc. of 120 mEq/L and an excess body water of about 5 L.
The primary goal is to increase and sustain the EC Sodium Concentration
(ECNa_conc.) to its normal levels, which is about 140 mEq/L. At the same time, the
TBW should be decreased to its normal value of 40 liters as well as the EC & the IC
water volumes. The challenge is to achieve these goals in balance, since rapid correction
of severe hyponatremia can cause brain edema. The total duration will be 160 hours, or
20 decision rounds. The player should revise his decisions at each step, by making use
of the provided analysis tools. The decisions made by the player are: Dose Diuretic,
Dose Aquaretic (ADH-Antagonist), Isotonic Saline, Hypotonic Saline, and Hypertonic
Saline. Moreover, the player can change some of the game settings or impose water
restriction to the patient by varying the scenario. A more detailed description of the
game can be found in the user manual.
20
(structions...) Control Panel
DOSE DIURETIC
decision neu
interval [35] perioa
a a
DOSE ADH ANTAGONIST
Fluid Therapy
ISOTONIC SALINE
Key Indicators ....
Body Water
Units:
{mmHg}
{Liter]
{Liter]
Units:
[ml/min]
[mEq]
{mEq]
Graph
Units: Bi
)
ie]
[_moconrats ] { recowerbecsions | { vary Seni... }
Figure 6.4. Game/Control Panel Screen
21
6.4. Results of the Game Tests by Players
The game was played by five graduate students of Industrial Engineering
Department of Bogazici University. Each of these players played the game several times
and applied different strategies in their trials.
The following figures represent the dynamics of the key measures obtained from a
representative player. Figure 6.5, 6.6, and 6.7 display the dynamics of the player’s saline
infusion decisions, ECNa concentration, TBW, MAP, urine output, and hourly correction
rate, respectively.
As can be seen from the figures below, the representative player initially was unable
to prevent the decline of the ECNa concentration to levels below 115 mEq/L, but then he
succeeded to increase it to mildly hyponatremic levels towards the end of the game. He
used a combination of Aquaretics and Diuretics to increase urine flow via a decreased
UNa concentration, and also applied a combination of hypertonic and isotonic saline
during his trial. The TBW first increased by 1.5 L, and then it tended to decrease. At the
end of the game, the simulated patient still has about 4 L of excess water. The correction
rates were between their normal health limits during simulation. The player first wrongly
chose to give hypertonic solution without drugs, but this only resulted in a fall in ECNa
concentration and a rise in blood pressure. Hypertonic saline combined with urine flow
increasing drugs later caused an elevated sodium balance and negative water balance.
l
= tte ly MA
oF 190.
Too wo ‘ano 12000 160.00 00 400
ours
LAvPERTONIC 3% SALINE 2 \SOTONIC SALE 3 RY POTONIC SALINE areca Sodium Concentration mEq
Unie rac edu concentaton
Figure 6.5. a) Saline infusion decisions and b) Dynamics of ECNa concentration for
the representative player
Teta ody wat
My
Jean Arterial Pressure emi
0.
7 Normal MAP
HL
lili
300
rc) 300
T00 160.08
O00 32.00
Total body water
e400 wD
Hours
Mean arterial pressure
128 00
100
Figure 6.6. Dynamics of a) TBW and b) MAP
22
[Fens Output in curent Parody L Fiouty EcNa Con Upper Linz 2: Houry ECWa Carection Rate 3: Hauhy EE Wa Corr Lower Limit
HH
cy 96.00
fl aaa
t Tahoo ro) ry no rin rary Tatoo Ted
rine colectes Hourly conection of Extracellarsoslum concentration
Figure 6.7. Dynamics of a) urine output and b) hourly ECNa correction rate
There is no single correct set of decision for players, but they should take into
account certain critical measures during their trials. As mentioned before, the correction
rate is a vital concern while correcting the hyponatremia of the patient. The two goals of
the treatment should be considered concurrently: attaining a negative water balance and
replenishment of the sodium deficits. Diuretics may be useful in correcting the excess
body water; but should be supported by high amounts of sodium. Therefore the players
that used Diuretics instead of Aquaretics had to administer high amounts of saline.
On the other hand, Aquaretics may decrease the UNa concentration to levels below
its normal; however Diuretics can only blunt the urinary concentration process, so they
can decrease the UNa concentration at most to its normal level. Generally players
administered Diuretics and Aquaretics together, and thus Diuretics reduced the effects of
Aquaretics in these trials. This demonstrates that Diuretics should not be administered in
severe cases of hyponatremia.
Another important point to note is the EC sodium level of the patient. Since the
sodium preserving systems are intact in an SIADH patient, the ECNa content is
preserved at a lower steady state value. However sodium depletion may worsen the
condition of the patient, both due to decreased sodium, and due to decreased urine flow.
Normally, SLADH patients have a normal or slightly elevated MAP level, and this level
should be closely monitored. Low MAP levels may inhibit the urine flow increasing
strategies, and a very high level of MAP is also unwanted due to its negative
consequences.
We now focus on a comparative evaluation of some key performance measures
for the players. Figure 6.8 displays the ECNa concentration with respect to the
corresponding trials of these five players. Player 1 first decreased and then slowly
increased the ECNa concentration. Player 4 did not change the ECNa concentration
noticeably, and player 3 decreased it. The trials of players 2 and 5 were the most
successful ones; Player 5 continuously increased the ECNa concentration, however
player 2 could not sustain the elevated level towards the end of the game.
In general, the TBW shows a variable decreasing trend for the 5 players as can be
seen from the graph in Figure 6.9, except player 3. Figure 6.10 depicts that the MAP
levels for the players stay close to normal levels, except players 1 and 3. Player 3 had
23
fluctuating high levels of MAP. On the other hand, player 1 had the highest levels of
MAP during his trial, and also he ended with the second lowest level of ECNa
concentration. Figure 6.11 displays the hourly correction rate of the ECNa concentration.
As can be seen, all the players acted patiently throughout their simulation except player
3. Figure 6.12 displays the sodium intake decisions of the players. Among the two
successful players, player 2 used a constant high amount of hypertonic saline, whereas
player 5S used graded amounts of saline. However the amount of sodium lost is
consistently high for the Pa player. On the other hand it stays at low levels for player 5
and does not increase further with increasing sodium intake. Since player 3 administered
a high amount of isotonic saline on the 76" hour, both the ECNa and the body water
increased abruptly and simulation stopped due to coma resulting from exceeding of the
hourly correction limits.
145
—o—playert
a player2
players
players
we players
normal
ECNa conc
120 De
us +
110
Figure 6.8. Dynamics of the ECNa concentration for five players
48
47
46 —eplayerl
3 45 —— —l- player2
s 44 — —player3
2 43 player4
@ 42 —* players
41 —®—normal
40 |@-@-8-O-0-€-0-6-0-8-0-8-0-0-6-0-0-0-060
39
SPH SF HS LW Pw ©
hours
Figure 6.9. Dynamics of the TBW for five players
24
0,7
0,5
—e—playerl
—a—player2
——player3
——player4
—*-— player5
Low er Limit
hourly conection rate
—— Upper Limit
hours
Figure 6.10. Dynamics of the hourly ECNa correction rate for five players
130
125
120 — playerl
115 —m- player2
F uo | ——player3
——playera
105 = players
100 —e—normal
95
90
SP He FP LY HP SO
hours
Figure 6.11. Dynamics of the MAP for five players
450
400
350
300 \—e—playerl
| 556 —m~player2
|——player3
‘g 200
3 J—=—=player4
150 =e players
100
50
0
op P Pv GS Pr Pw SH
hours.
Figure 6.12. Sodium intakes resulting from decisions of five players
7, CONCLUSIONS AND FURTHER RESEARCH
The purpose of this research is to study the normal and disease physiology of the
body water metabolism, and to develop an interactive simulation model for a particular
body fluid disorder, namely water intoxication/hyponatremia. For this purpose, a
system dynamics model is built representing the structure of the body water and sodium
balance for a normal individual. Then, this model is modified to include the effects of
disease processes, and example dynamics are reproduced for the development of ADH-
induced hyponatremia. Finally, a game version of the modified model is constructed by
including the most relevant treatment options, and necessary measurements for
diagnosis. The game is then used as an experiment platform to test the possible effects
of a given set of treatment options on a simulated patient. This interactive simulation
game attempts to be a step towards a closed-loop therapy for the hyponatremia patients.
It can also be used as a learning and teaching environment for the renal physiology, and
especially for the differentiation between the concepts of “sodium content” and
“sodium concentration”, and related disorders.
As a result of extensive validity testing, the model is found to be a robust
representation of the water-electrolyte balance in normal and various test conditions.
The model demonstrates that ADH (Antidiuretic Hormone) is extremely important for
the control of sodium concentration, yet it has a relatively mild effect on the control of
blood volume/pressure. On the other hand, arterial pressure is mainly determined by
“sodium intake”, rather than water intake, which at first seems paradoxical, since
arterial pressure is in fact determined by the “water volume” of the EC compartment.
The modified model for the development of hyponatremia reproduces all the
cardinal features of the SIADH (Syndrome of Inappropriate Antidiuretic Hormone
Secretion). Dysregulated ADH-thirst system first causes an increase in the body fluids,
but then transient sodium loss is promoted, and the extracellular fluid volume is only
slightly elevated, despite the apparent expansion of the body water. Hence, it is the
intracellular compartment which is mostly expanded in SIADH. As a result of dilution,
extracellular sodium concentration falls drastically, but the arterial pressure is only
slightly elevated. Moreover, urine is still highly concentrated due to the absent negative
feedback between the extracellular sodium concentration and the ADH.
The interactive simulation game version yields meaningful results for various
treatment options. Game results reveal that the effective correction of the SIADH can
only be attained if a negative water balance can be maintained. Replacing the sodium
deficits alone is worthless since blood pressure conserving mechanisms cause an
increased sodium excretion rate following the intake. Moreover, it is demonstrated that
graded doses of hypertonic saline infusion is the most useful solution for the treatment.
However it should be administered carefully to prevent an overcorrection, and
concurrently with drugs that increase the urine flow. In conclusion, the model and the
game version constitute an experimental laboratory for a closed-loop therapy approach
to hyponatremia.
There are several avenues in which this research can be expanded. One first step is
converting the current game model for the treatment of severe hyponatremia in an
26
intensive care unit setting, by changing the initial conditions of the modified model and
the treatment options. Moreover, more realistic initial conditions could be selected to
represent a person who is inclined to become hyponatremic.
Since the focus of the modified model is the development and therapy of
hyponatremia, other electrolytes have not been analyzed. However, hyponatremia
occurs with many other electrolyte imbalances, and hypokalemia is the most common
electrolyte disorder. An analysis of impacts of the treatment options of hyponatremia
on potassium dynamics may reveal a broader range of possible physiological
phenomena.
Another important electrolyte excluded from this study is the urea. We have
assumed that urine osmolality is only determined by the sodium chloride; however in
reality urea also contributes to 40 percent of the urine osmolality when the kidney is
forming a maximally concentrated urine (Guyton, 2000).
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30
