A Dynamic Simulator for the Management of Disorders of the ... · Karanﬁl and Barlas: A Dynamic...

OPERATIONS RESEARCHVol. 56, No. 6, November–December 2008, pp. 1474–1492issn 0030-364X �eissn 1526-5463 �08 �5606 �1474

informs ®

doi 10.1287/opre.1080.0618©2008 INFORMS

A Dynamic Simulator for the Management ofDisorders of the Body Water Homeostasis

Özge KaranfilChronic Disease Systems Modeling Laboratory, School of Kinesiology, Simon Fraser University, Burnaby,

British Columbia, Canada V5A 1S6, [email protected]

Yaman BarlasDepartment of Industrial Engineering, Bogazici University, Istanbul, Turkey, [email protected]

A dynamic model is built to study the water regulation of human body and related disorders, focusing on the fundamentalfeedback mechanisms involved in their normal and abnormal physiology. The simulation model is extended to includetherapeutic interventions related to the most common body fluid disorder, namely, water intoxication/hyponatremia. Themodeling approach is based on system dynamics methodology. Comparisons with experimental and field data show thatthe model adequately reproduces typical dynamics of the body fluid variables in their normal and diseased states. Finally,an interactive game version is developed to test the possible effects of alternative treatment options on a simulated patient.Simulation and game results reveal the subtleties involved during and after administration of various pharmacologicalinterventions. For example, hypertonic saline should be administered concurrently and in delicate balance with drugs thatincrease urine flow. The simulator offers a virtual laboratory for experimental research and education on diagnosis andalternative therapies of body water disorders in general and hyponatremia in particular.

Subject classifications : simulation: system dynamics; health care: diagnosis/treatment; games.Area of review : Special Issue on Operations Research in Health Care.History : Received December 2006; revisions received November 2007, March 2008, May 2008; accepted June 2008.

What am I, Life?A thing of watery saltHeld in cohesion by unresting cells,Which work they know not why, which never haltMyself unwitting where their master dwells,I do not bid them, yet they toil, they spin � � �

John Masefield, “What Am I, Life?”

1. IntroductionHippocrates held the idea that disease is cured by natu-ral powers, but the term of “homeostasis” was first usedfar later by Walter Cannon, in his book The Wisdom ofthe Body (1932). Cannon made a qualitative use of theconcepts of today’s dynamic systems theory and suggestedthat physiological systems are dominated by negative (com-pensating) feedback loops. Another pioneer of systemsapproach to physiology, Arthur C. Guyton, was the firstto introduce the concept of systems analysis to physicians(Guyton et al. 1972), whose approach then led to the emer-gence of biomedical engineering. Recently, there has beena growing interest in the modeling and OR communityto provide model support in personalized diagnosis andtreatment of some important diseases: Agur et al. (2006)develops a method for optimal patient-specific chemother-apy scheduling for cancer treatment. Similarly Romeijinet al. (2006) uses a new linear programming approach

to determine optimal radiation treatment plans for cancerpatients. Ryu et al. (2004) utilizes a mathematical program-ming technique called isotonic prediction in disease prog-nosis and illustrates it on two medical applications. Craftet al. (2005) builds a comprehensive system of a differ-ential equations model to understand how best to respondto a bioterror anthrax attack. Abdel-Hamid (2002) mod-els the dynamics of human energy regulation using systemdynamics simulation and studies the implications for alter-native obesity treatments. Other recent applications of sys-tem dynamics and systems science to health care includeHirsch and Immediato (1999), Bar-Yam (2006), Sterman(2006), Jones et al. (2006), and Incioglu (2007).Our focus in this paper is the system of regulation

of body fluids, which is critical to control diseases suchas hypertension and dysnatremia (dehydration and waterintoxication being two examples). Early models that repre-sent certain aspects of renal control of body fluids belong toDeHaven and Shapiro (1967), Reeve and Kulhanek (1967),and Toates and Oatley (1970, 1977). Integrated models ofbody fluid regulation that also consider the circulatory sys-tem include those by Ikeda et al. (1979) and Abbrecht(1980). The drinking mechanism developed by Reeve andKulhanek (1967) forms the basis of the main approach andassumption regarding the drinking structure in our study, aswill be seen later in §3. Finally, the most complete analysisof body fluid dynamics belongs to Guyton and coworkers,

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Karanfil and Barlas: A Dynamic Simulator for the Management of DisordersOperations Research 56(6), pp. 1474–1492, © 2008 INFORMS 1475

who constructed an overall circulatory model for examin-ing the causes of hypertension (Guyton and Coleman 1967,Guyton et al. 1972). Uttamsingh et al. (1985) extended hismodel for the clinical application of patients with renalfailure. Recently, a cardiovascular system model was devel-oped by Karaaslan (2004), integrating the previous mod-els developed by Guyton et al. (1972), Uttamsingh et al.(1985), and Coleman and Hall (1992). The fundamentalwater and sodium regulation mechanism described in thisseries of publications by Guyton and coworkers has beenan important contributor to the foundations of our model.In §3, we shall more specifically refer to these publicationsin places where concrete results by prior modeling researchhave been used in our work. But as will be seen, our modelis different enough from these prior models in purpose,time frame, and aggregation level, implying that we had towrite our own original equations to a large extent. Perhapsthe greatest utility of the prior modeling and physiologyliterature has been in their numeric and/or qualitative datathat we used in estimating the parameters of our equations.The homeostatic regulation of body fluids is important

in almost every field of medicine. In health, total bodywater and its distribution in the body is maintained betweennarrow limits. This task is accomplished by two distinctbut interactive feedback systems: The main feedback sys-tem for body water regulation is the thirst-AntidiureticHormone (ADH) system, and the main feedback mecha-nisms for sodium balance include the Aldosterone (ALD)and the Atrial Natriuretic Hormones (ANH), and the renalmechanisms (Guyton and Hall 2000).Problems associated with body fluid disorders are very

common in hospitalized patients. Among these, waterintoxication (or hyponatremia) defined as an abnormallylow level of extracellular sodium concentration, is the mostimportant body fluid disorder with the potential for signifi-cant mortality. Extreme cases of low sodium concentrationand high body water content may have serious conse-quences. The treatment of hyponatremia constitutes a prob-lem, partly because all available therapies have significantlimitations. Furthermore, it is observed that a large portionof hyponatremia incidences are in fact “hospital-acquired.”Most of these patients acquire hyponatremia as they receiveintravenous fluids, which is a very common practice in hos-pitals. Today, more than 75% of currently recommendedintravenous fluids are in the form of electrolyte-free water,which is known to aggravate hyponatremia (Halperin andBohn 2002). This situation has raised concerns abouthyponatremia, and inspired many studies on its diagnosisand optimum therapy (Shafiee et al. 2003).Due to the feedback complexity of the underlying struc-

ture and its interactions with various pharmacological ther-apies, body water regulation and its disorders constitutea suitable area for system dynamics modeling. However,no closed-loop, systemic therapy approach for disorders ofdysnatremias has yet been attempted (Northrop 2000). Ourstudy builds a closed-loop system dynamics model of body

water regulation and its disorders, focusing particularly onhyponatremia.

2. Clinical Abnormalities of BodyFluid Regulation

Any influence that alters the balance of the body wateror sodium metabolism inevitably affects the balance of theother. It is important to differentiate the dynamics and clin-ical abnormalities of extracellular (EC) fluid volume and/orsodium content from those of the total body water.

2.1. Disturbances of Body Sodium Content

As the main substance of the EC fluid, the sodium contentdetermines the EC fluid volume. Therefore, disorders ofsodium metabolism are always manifested as disorders ofvolume status. Moreover, mean arterial pressure (MAP)is also affected due to the close interrelationship betweenEC fluid volume and the MAP. Disorders of sodiummetabolism commonly coexist with disorders of water andfluid-electrolyte balance.

2.2. Disturbances of Water Metabolism:Dysnatremias

Disorders of water metabolism are clinically manifestedby disorders of EC sodium concentration (dysnatrem-ias) because the regulatory systems controlling watermetabolism do so by maintaining a constant EC sodiumconcentration. Loss of water leads to hypernatremia andwidespread functional disturbances in the brain. On theother hand, accumulation of water leads to hyponatremia,cell swelling, and disturbances in the central nervoussystem.In general, failure to maintain body water within nar-

row limits is associated with two functions. The first oneinvolves the capability to dilute or concentrate urine appro-priately, and the second one is associated with the thirstfunction. If one of these components fails to function prop-erly, the other one may still compensate for this failure(Jamison and Oliver 1982).Hyponatremia is the most common and potentially seri-

ous electrolyte abnormality in hospitalized patients (Shafieeet al. 2003). It is defined as an EC sodium concentration ofless than 135 mEq/L. The most common causes of hypona-tremia are the Syndrome of Inappropriate AntidiureticHormone Secretion (SIADH) (38%), incorrect hydration(19%), and continuous diuretic treatment (30%) (Halperinand Bohn 2002).

3. Description of the ModelThe purpose of this modeling study is to develop adynamic representation of the body fluid balance in nor-mal and pathological states so as to test alternative treat-ment strategies of dysnatremia. The study has three mainparts, corresponding to three research goals: (1) to offer

Karanfil and Barlas: A Dynamic Simulator for the Management of Disorders1476 Operations Research 56(6), pp. 1474–1492, © 2008 INFORMS

a dynamic model that explains the main feedback mecha-nisms involved in the normal physiology/stability of bodywater balance and osmolality, (2) to extend the model togenerate common medical disorders of body water regu-lation, namely, dysnatremias, and (3) to explore effectivetreatment strategies for a virtual patient with acute hypona-tremia. For this last purpose, an interactive game version ofthe model is constructed whereby players can interactivelytest their own strategies by simulated experience. (Exten-sive gaming experiments by players with different back-grounds, carried out with suitable design of experimentsand statistical analysis is our ongoing research.)Two major systems that are involved in the homeostatic

regulation of body fluids are the system that regulates theosmolality/body water and the system that regulates theblood volume/sodium content. In this study, the central con-troller is the hypothalamus, and thus the normal values ofthe main regulated variables are taken as exogenous con-stants, e.g., the set point for ADH (Antidiuretic Hormone)and the set point for blood volume.The model is built using a system dynamics approach

(Sterman 2000, Barlas 2002). According to this method,the dynamics of a system are represented by formulatingthe rates of changes (or flows) of a set of stock (or state)variables. Converters are intermediate variables linking aflow (or a converter) variable to other variables at somepoint in time. A system dynamics model thus consists of aset of coupled differential/difference equations. The generalforms of equations are:

d

dtStock = inflows− outflows�

Flows= f �stocks� converters� flows��

Converters= f �stocks, converters, flows��

Simple examples of these three types of variables in ourmodel (to be discussed later) are:

d

dtADHinPlasma= Actual_ADH_Release

− ADH_Clear �a stock equation��

Actual_ADH_Release = Desired_ADH_Release

× Eff _of _ADH_Avail

(a flow of the above stock)�

Eff _of _ADH_Avail = f �ADH_Pool�MaxPoolCapac�

(a converter equation)�

where f �·� will be specified in the complete model as alogistic function reaching a saturation level.A typical model consists of many equations and functions

f �·� most of which may be nonlinear and/or time-delayed.

Such set of nonlinear, delayed differential/difference equa-tions are almost always impossible to solve analytically.That is why simulation is an integral part of the methodol-ogy. Models are presented typically as stock-flow diagrams(in which stocks are represented by boxes and flows byvalves). The polarity of causal relations and feedback loopsbetween variables are presented in causal loop diagrams.(See Figures 3.1 and 3.4 for examples.)Our model is composed of nine sectors grouped under

five sector groups. These sector groups correspond tobody water, sodium, hormonal system, urinary sodium con-centration, and treatment. The initial states and param-eters (see the online supplement that can be found athttp://or.journal.informs.org/) are standard values typicallyused in the major medical textbooks and in earlier models.When available, published experimental data are used. Themodel assumes a standard healthy human male of 70 kgwith 40 liters of body water.

3.1. Regulation of Total Body Waterand Osmolality

The mechanism for the regulation of water balance is oftenreferred to as the “thirst-Antidiuretic Hormone (ADH)mechanism.” The two most important factors that are mon-itored by this mechanism are extracellular (EC) osmolalityand blood volume. EC osmolality represents the number ofparticles in a given mass of water, usually expressed as mil-limoles (or milliequivalents) per kilogram of water. In usualconditions, control of EC osmolality is almost the sameas controlling the EC sodium concentration because ECsodium is the substance that mostly contributes to the ECosmolality. Its importance in terms of water balance is thatthe control of EC osmolality indirectly controls intracellu-lar (IC) volume. (Three facts about the body water/sodiumare relevant: first, “mobile” sodium is mostly restricted tothe EC fluid; second, intracellular solute does not changeeasily; and third, EC osmolality must equal IC osmolalityexcept for very fast transients.) It should be noted that themechanisms that control the EC sodium “concentration”and the EC sodium “amount” are different, albeit interact-ing (Bagby and Bennett 1998). EC sodium concentrationhas a normal value of 142 mEq/L, and is found by divisionof EC sodium content (ECNa) by EC fluid volume.Figure 3.1 provides a simplified version of the stock-

flow diagram of the body water/osmolality control sectorof our model. The first and the second control (negative)loops demonstrate the ADH-thirst feedback mechanism forEC osmolality and body water control. An increase in ECosmolality raises the level of ADH, and as a consequenceof increased urinary concentration, water excreted in urinedecreases. At the same time, thirst perception is stimu-lated and water intake is increased. It is assumed that stim-uli acting on ADH secretion do so as an additive sum,and the response of ADH takes effect immediately (Toatesand Oatley 1977). GFR (Glomerular Filtration Rate) rep-resents the amount of filtrate formed per minute, so it


Figure 3.1. Simplified stock-flow diagram for body water/osmolality control.

Total body water(TBW)

Extracellular fluidvolume (ECFV)

+

Extracellular sodiumconcentration

–

1–

2–

Glomerular filtrationrate (GFR)

Filtered sodiumload

+

+

4–+

+

3–

–

Bloodvolume/pressure

+

+

5+ –

+

–

Drinking+

ADH clearance

+

+–

Antidiuretichormone (ADH)

Urine flow

Urine sodiumconcentration

Sodium excretedin urine

ADH release

determines the amount filtered for any substance in thekidney. An increase in GFR increases urine flow via adecreased urinary concentration (third loop). As seen in thediagram, GFR and the EC sodium concentration influencethe sodium excretion rate by influencing the filtered sodiumload (fourth and fifth loops).Drinking is considered as the only source of fluid intake.

Both continuous and discontinuous-periodic drinking aremodeled as options to simulate the drinking behavior. In ei-ther case, there is a 1/2 to 1 hour delay for all of the waterdrunk to become distributed in the body (Northrop 2000).The model developed by Reeve and Kulhanek (1967) formsthe basis regarding the drinking structure. Accordingly, thediscontinuous drinking version of the model represents aswitch-on and switch-off structure, which only acts undersome threshold body water level, and this level is main-tained within ±0�5 L of a mean (Reeve and Kulhanek1967). For the continuous drinking structure, the drinkingrate is approximated as a variable that may vary aroundits normal value, depending on varying levels of the ECosmolality (see Figure 3.2):

UnrestrictDrinking=NormalDrinking

× Eff _of _ECOsm_on_Drinking�

A constant insensible water loss, which represents thecontinuous escape in the form of evaporation (about0.9 L/day), and a variable urination flow represent the

two sources of loss of water from the body. The urinaryexcretion can be divided into a constant component anda variable “free water excretion.” The constant rate or theMinUrineFlow is referred to as the obligatory urine loss,which is necessary to clear out the wastes of the body andit is imposed as a constraint. Consequently, the equationfor the UrineFlow becomes

UrineFlow=MAX�MinUrineFlow, ImpliedUFlow��

The urine flow rate is in turn determined by two variables,i.e., the urinary sodium concentration (UNaConc) and therate of sodium excretion (NaOutUrine). The implied urineflow rate is linearly related to sodium excretion because therate of water transport is always proportional to the rate of

Figure 3.2. Effect of EC osmolality on drinking.

10.00

10.0010.00

0.2000.000

–10.00–10.00

eff ofECOsm on

drinking


Figure 3.3. Effect of ADH on urine sodium concen-tration.

12.00

0.000

0.000 3.0000.000 3.000

eff of ADH

ADH ratio to normal

solute transport (Guyton and Hall 2000). The equation ofthe ImpliedUFlow is

ImpliedUFlow= NaOutUrine

UNaConc× 1�000�

The above equation depicts the inverse relationshipbetween urine osmolality and urine flow rate (assuming agiven sodium outflow). Ordinarily, the urine flow rate ×urine osmolality (equal to the amount of solute excreted) isrelatively constant and independent of flow rate (Bray et al.1989). Thus, the kidney adjusts the urine flow rate withoutmarkedly affecting its handling of sodium and other solutes.The capability to dilute or concentrate urine appropri-

ately depends on various factors; however, under normalphysiological conditions, the ADH level is the main deter-minant of urine osmolality (Guyton and Hall 2000). ADHinfluences water excretion by promoting concentration ofurine, but the Na+ excretion is unaffected by ADH. Accord-ingly, the effect of ADH on urine concentration is for-mulated with a decreasing sigmoidal graphical function(see Figure 3.3).From the graph, it can be seen that the renal response to

ADH saturates when ADH concentration reaches approx-imately three times its normal level, after which urinaryosmolality is maximal and cannot increase further despiteadditional increases in ADH levels. With maximal concen-trations of ADH (maximal antidiuresis), as little as 0, 4–0,5 L of urine may be excreted per day with a urine osmo-lality of about 1,200 mEq/L (Bray et al. 1989, Janicic andVerbalis 2003.) It can also be seen that even when ADH istotally absent, the maximum amount of urine to be excretedcannot increase indefinitely.On the other hand, there is a combination of factors other

than ADH, i.e., the Glomerular Filtration Rate (GFR), thatact in the absence or presence of ADH and change the uri-nary concentration, which is an indicator of the complexityand importance of the urinary concentration dynamics.Accordingly, the UNa concentration implied by ADH

and GFR (ImpliedUNaConc) is calculated by the followingeffect formulation:

ImpliedUNaConc= ImpliedUNaConcByADH

×Eff _of _GFR_on_UNa�

where

ImpliedUNaConcByADH = NormalUNaConc

Eff _of _ADH�

3.2. Regulation of Total Body Sodium andExtracellular Fluid Volume

In the average adult human, about five-eighths of thebody fluids constitute the intracellular (IC) fluid and three-eighths remain extracellular (EC), or 25 liters are IC fluidand 15 liters are EC. Sodium is the principal determinantof the total EC fluid volume (ECFV). Indeed, the humanbody regulates the ECFV by regulating its Na+ content(Bray et al. 1989). Because the EC and the IC osmolalitiesare always equal (except for very short transients) and thetotal “mobile” Na+ and K+ are mostly kept in their respec-tive compartments, the ECFV is derived by the followingequations:

ECNa

ECF V= ICK

ICF V� where

ECF V + ICF V = TBW� yielding

ECF V = TBW × ECNa

�ECNa + ICK�

/1�000�

Maintenance of normal ECNa and thereby a normalECFV requires a refined intake and excretion for Na+ ions.However, related literature suggests that the regulated com-ponent has to be sodium excretion because regulation ofintake, i.e., the sodium appetite regulation in modern soci-eties, mostly depends on habits rather than the requirementand is almost always greater than necessary for homeosta-sis. Therefore, the sodium intake rate is assumed to beconstant in the base model. Sodium excretion is affectedby various factors; however, only the most important onesare explicitly represented in the model: the Glomerular Fil-tration Rate (which affects the filtered load of sodium inthe kidney), the Renin-Angiotensin-Aldosterone hormonesystem, and the recently found Atrial Natriuretic Hormone.Figure 3.4 shows our simplified stock-flow diagram

depicting the causal mechanisms related to these three fac-tors. The first and the third loops are related to balancingthe effects of the filtered load. Filtered load refers to therate at which substances are filtered in the kidney. It isfound by the equation: GFR × Plasma Concentration ofthe substance (Guyton and Hall 2000). For any substance,the amount excreted in the urine is the algebraic sum of theamounts filtered, reabsorbed, and secreted by the tubules.Any change that causes an increase in the filtered load ofsodium causes a rise in sodium excretion. On the otherhand, the second loop indicates that an increase in ECNaalso has a decreasing effect on ECNa concentration dueto the fluid shift between the IC and the EC compart-ments. The other balancing loops relate to the effects of theANH and ALD hormones on reabsorption of Na from thekidneys. The response of ANH is assumed to take effectimmediately; however, ALD is effective only in long-termadjustments of sodium excretion (Bray et al. 1989).


Figure 3.4. Simplified stock-flow diagram for sodium and EC fluid volume regulation.

–

+

6– +

+

+

1–

5–

2–

+

+

+

–

3–

4–

7 –

+

–

+

+

–

–+

+

+

+

+

–

+

–



Blood volume(BV)

Mean arterialpressure (MAP)

AtrialNatriuretic

Factor(ANH)

ExtracellularSodium (ECNa)

eff of ANH

desired ANH

ECNa ratio tototal

Na intake

Na out in urine

Filtered Na load

desired ALD

Aldosterone(ALD)

eff of ALD

Renin

ECNa conc

ANH adjustment

ALD adjustment

Sodium excretion rate (NaOutUrine) is formulated bya multiplicative effect formulation. The effects of ALDand ANH on sodium excretion are formulated with graphi-cal functions with reference to their normal concentrations(see the online supplement for all functions):

NaOutUrine= FilteredNa×NormalFraction

× Eff _of _ANH_on_NaExcret

× Eff _of _ALD_on_NaExcret�

where

FilteredNa= GFR ×ECNaConc/1�000�

It is clear that changes in GFR or ECNa concentrationwill change the sodium load presented to the kidney. Undernormal conditions, 99% of the filtered sodium is reabsorbedback to blood. Therefore, the filtered load is multiplied bya normal fraction to find the normal sodium excretion rate.

3.3. Integrated Regulation of Body Waterand Sodium

Figure 3.5 gives an overall summary of how the two con-trol systems of body water and body sodium integrate toproduce a tight control system. This diagram may alsohelp to differentiate the clinical abnormalities of EC fluid

volume/sodium content regulation from abnormalities ofbody water/osmolality.In SIADH (Syndrome of Inappropriate Antidiuretic Hor-

mone Secretion), the degree of water retention is limiteddue to the adaptive mechanisms of the body. The patho-physiology of this disease can be better understood whenthe causal-loop diagram presented in Figure 3.5 is exam-ined. Main features of the SIADH are drastically decreasedEC sodium concentration, a clinically normal EC fluidvolume, normal/mildly elevated blood pressure, and anincreased glomerular filtration rate (Schwartz et al. 2001).It is seen that the EC/blood volume regulation is appropri-ate; however the osmolality/TBW regulation is deranged.As the total body water increases due to increased ADHlevels, both the EC and the IC volumes increase. How-ever, a transient natriuresis induced by the ANH and ALDhormones acts to defend the EC volume. Therefore, mostof the excess fluid is accumulated in the IC fluid. A mildelevation in glomerular filtration rate can be considered asan adaptive response of the body to compensate the highurinary concentration induced by ADH. (SIADH will besimulated and discussed again in §4.4.2.)

4. Validation and Analysis of the ModelThe model is simulated in Stella software (isee Systems,Inc., http://www.iseesystems.com). The basic time unit is


Figure 3.5. Overall regulation of body fluids by integrated control of body water and body sodium.


+

Na out in urine

ECNa conc

–

–

+ –

–

+

UNa conc

Drinking

+

–

+

+


–Filtered na load

+

+

+

–

–

ECNa ratio tototal

+

–

+

+

+

+

–

––

–

–

–

–

+

–

+

+

+

Atrialnatriuretichormone

(ANH)

Extracellularsodium(ECNa)

Antidiuretichormone

(ADH)

Intracellular fluidvolume (ICFV)

Total bodywater (TBW) Mean arterial

pressure (MAP)

Aldosterone(ALD)

Urine flow (UFlow)

hours and a sufficiently small time step (1/32 hr.) is used toassure numerical accuracy in simulation. Because some ofthe system behavior becomes evident only in the mediumterm, the simulation time horizon is set somewhere between24 and 72 hours in most runs. (It is as high as 500 hours insome scenarios where long-term dynamics are of particularinterest.) A formal validation process is followed to detectany structural flaws of the model (Barlas 1996). Numer-ous direct structure tests are performed during model build-ing, which are not presented here due to space limitations(see Karanfil 2005). Validation of the model is next demon-strated by performing “structure-oriented behavior tests”(indirect structure tests), such as extreme condition andbehavior sensitivity tests (Barlas 1989, 1996), and selectedillustrations are presented below. Finally the model behav-ior is also compared with the real data, to the extent thatexperimental or field data are available, as will be seenbelow.

4.1. Validity of the Output Dynamics of the Model

4.1.1. Base Behavior of the Model. Both continuousand discontinuous drinking options are modeled to simulatethe drinking behavior of humans. When all its stocks areinitialized ideally at their equilibrium values, the continu-ous version of the model correctly shows a constant equi-librium behavior, and the discontinuous drinking version

demonstrates the normal periodic variations in the keyvariables around the equilibrium points (see Figure 4.1).Discontinuous-periodic drinking represents a switch-on andswitch-off structure that only acts under some thresholdbody water level, which is a more realistic representationof the drinking behavior. The EC sodium and the meanarterial pressure show almost no change during the day.The ECNa concentration varies between 141 mEq/L and143 mEq/L, which is a small variation. The main changecan be seen in the dynamics of the urine flow, drinking, theurine concentration, and ADH. Because water is continu-ously lost and then replenished by drinking, ADH adjuststhe urine concentration to prevent higher fluctuations inthe ECNa concentration in the case of highly varying fluidintake. ADH can thus be quite variable under normal con-ditions. As a result, the total body water (TBW) is main-tained within the normal limits. The above equilibrium runs(both continuous and discontinuous-periodic) are obtainedprimarily as a demonstration of the structural validity ofthe model. Output behavior validity is discussed in the fol-lowing sections.

4.1.2. Water Loading. Examining the dynamics ofbody fluids after water loading constitutes an extreme(“stress”) test (Barlas 1996) to assess the validity of inter-actions between body fluids and related hormones in themodel. For this simulation, the NormalDrinking variable is


Figure 4.1. Equilibria of the key variables with (a) discontinuous-periodic drinking, (b) continuous drinking.

0.00 6.00 12.00 18.00 24.00

0

2,000

4,000

0

6,000

12,000

0

125

250

140.0

150.0

160.0

1: Drinking 2: ADH in plasma 3: Urinary Na conc 4: ECNa conc

1 1 1 1

2

2

2

23

3

3

3

4

44

0.00 12.00 36.00 48.00

Hours

37,000

39,000

41,000

138

144

150

0

125

250

80

95

110

50

100

150

1: TBW 2: ECNa conc 3: UNa conc 4: MAP 5: Drinking

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

(a)

(b)

4

24.00

set to zero, and a pulse of water input of 1,000 ml is givenat time 0. The urine flow rate increases by about 11 foldin one hour, and after three hours it returns to its normalvalue. The validity of model behavior in this case is demon-strated by comparing its output behavior against real data(see Figures 4.2 and 4.3).Figure 4.4 gives a schematic representation of the nor-

mal physiologic relationships among EC osmolality, ADHconcentrations, urine osmolality, and urine volume, basedon real data. Accordingly, urine osmolality is proportionalto plasma ADH levels, but urine volume is inversely relatedto urine osmolality.The model-simulated results on the relationship between

the urine flow and the urine sodium concentration in the

base run and in the water-loading scenario are given in Fig-ure 4.5, again agreeing with empirical evidence providedin Figure 4.4.

4.2. Experiments with Changes inDaily Water Intake

Exploring the dynamics of body fluids after changing thewater intake provides a tool to disturb the model from itsequilibrium and test the validity of the resulting behav-ior. So, this set of experiments is simulated by varying thedaily water intake (NormalDrinking) of the person from itsnormal value, which is about 2.2 liters, and resetting thethirst feedback on drinking. The main effect of an increased


Figure 4.2. Urine flow rate following ingestion of 1 Lof water; (a) data from Baldes and Smirk(1934), (b) data for eight subjects, (c) datafor one subject (Uttamsingh et al. 1985).

12

8

4

00 1 2 3

Time, h

0 1 2 3

Time, h

0 1 2 3Time, h

Urin

e flo

w r

ate,

ml/m

in

12

8

4

0Urin

e flo

w r

ate,

ml/m

in

Urin

e flo

w r

ate,

% in

crea

se 1,500

1,000

500

0

(a) (b)

(c)

Note. Reproduced with permission from the IFMBE.

(or decreased) water intake is a big fall (or rise) in the urinesodium concentration and a consequent rise (or fall) in theurine flow. There is almost no change in the total bodywater, mean arterial pressure, and the EC sodium, as longas the fluid intake and the fluid loss are precisely balanced.So, these critical indicators of the body are not sensitive toan increase or decrease in water intake, which is a demon-stration of the resilience of the negative feedback structure.Representative dynamics of the key variables in responseto doubling the normal drinking value to 4.4 liters/day aregiven in Figure 4.6.

Figure 4.3. Simulated urine flow following ingestion of1 L of water for comparison against realdata of Figure 4.2.

0.00 1.00 2.00 3.00 4.00

1.0

6.5

12.0

1.0

3.0

5.0

2: Na excr ratio

1

1

1

122 2 2

1: Urine flow rate ml\min

Hours

Figure 4.4. Normal physiologic relationships amongEC osmolality, ADH (also termed ArginineVasopressin or AVP) concentration, urineosmolality, and urine flow in man (fromVerbalis 2003).

10

9

8

7

6

5

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280

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284

286

288

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1,200

1,000

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600

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200100

Urine volume (L/day)

292

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Plasmaosmolality

(mOsm/kg H2O)

0 4 8 12 16 20 240

0.5

PlasmaAVP

(pg/ml)

Thirstosmotic

threshold

AVPosmotic

threshold

Urineosmolality

(mOsm/kg H2O)

Note. Copyright Elsevier (2003). Reproduced with permission.

4.2.1. Sensitivity of Blood Volume to Different Levelsof Daily Water Intake. Under normal conditions, bloodvolume is not affected by changes in fluid intake (Guytonand Hall 2000). Real-world data in Figure 4.7(a) demon-strate the fact that the blood volume remains almost con-stant despite extreme changes in water intake—the powerof homeostasis. The simulated results of Figure 4.7(b) areagain in accordance with this empirical evidence fromGuyton and Hall (2000).

4.3. Experiments with Changes in DailySodium Intake

Similarly, changing the sodium intake presents another testto explore the validity and limits of the body water andsodium control feedback mechanisms of the model and tovalidate its behavior against empirical data. Thus, this set ofexperiments is simulated by varying the daily sodium intakeof the person from its normal value. The results demon-strate that changes in sodium intake have very little effecton the ECNa concentration and the TBW, but they havea greater effect on the urine concentration, drinking, and


Figure 4.5. Simulated relationships between urine osmolality and urine flow (a) for the base run, (b) after ingestion of1 L of water, to be compared with real data in Figure 4.4.

0 200 400

0

150

300

UNa conc vs. urine flow: 1–

Urine flow0 375 750

0

100

200

(a) (b) UNa conc vs. urine flow: 1–

Urine flow

urine flow. A representative dynamics of the key variablesafter a four-fold increase in sodium intake are given in Fig-ure 4.8. In this simulation, the EC fluid volume increasesby 5%, whereas the change in the ECNa concentration,IC fluid, and the TBW remains between 1%–2% becausewater is shifted between the EC and the IC compartments.Increased salt intake causes an increase in the ECNa con-centration, which stimulates thirst and increases drinking,and urine flow increases to match the elevated water intake.The resulting urine is much more concentrated than normal,

Figure 4.6. Dynamics of key model variables in case of increased daily water intake.

0.00 12.00 24.00 36.00 48.00 60.00Hours

40,000

40,150

40,300

2,110

2,120

2,130

100

102

103

45

90

135

50

150

250

1: TBW 2: ECNa 3: MAP 4: UNa conc 5: Urine flow

1

1

11 1

2

2

2

2 2

3

3

33 3

44 4 4 4

5 5 5 5 5

as expected; urine concentration and drinking increase byabout 100%. These results corroborate the prevailing the-ory in the literature: “Consequently, NaCl ingestion onlytransiently increases ECF volume and Na content. Even asustained increase in daily NaCl intake causes remarkablysmall increases in ECF volume/Na content (<5%)” (Bagbyand Bennett 1998, p. 171).

4.3.1. Sensitivity of ECNa Concentration to DifferentDaily Sodium Intakes. In a normal person, ECNa con-centration is controlled quite effectively even with large


Figure 4.7. (a) Approximate real (from Guyton and Hall 2000) and (b) simulated effects of changes in daily water intakeon the blood volume level.

6

5

4

3

2

1

0

0 1 2 3 4 5 6 7 8

Blood volume

Normal range

Death

Blo

od v

olum

e (li

tres

)

Daily fluid intake (water and electrolytes) (litres/day)

5.012

5.007

5.002

4.997

4.992

4.987

4.982

4.977

Daily water intake

1.3

1.7

3.0

5.0

7.0

Blood volume(a) (b)

Note. Guyton and Hall (2000) was published by W. B. Saunders in 2000 and reprinted by Elsevier-Saunders in 2006. Copyright Elsevier. Reproduced withpermission.

changes in sodium intake, as long as water intake is enoughto balance the losses (Guyton and Hall 2000). In this exper-iment, the effectiveness of body feedback mechanisms tocontrol the ECNa concentration is investigated. The sys-tem is initialized with all variables being at their normallevels, and sodium intake is varied by a factor of 0.2 to 5times normal salt intake, a range of 25-fold (the factors inbetween being 0.4, 0.6, 0.8, 1, 2, 3, and 4). It is seen thatECNa concentration remains remarkably within 1% controllimits when all feedback systems are intact (see Figure 4.9).In the second experiment, the effect of the ADH-thirst

feedback system on ECNa concentration is investigated.The above experiment is repeated by blocking the ADHand then the thirst control systems, and it is seen that eachof the ADH and thirst control systems can regulate the

Figure 4.8. Dynamics of key variables in the case of four-fold increased sodium intake.

0.00 7.20 14.40 21.60 28.80 36.00

125

188

250

142

149

155

15.00

17.50

20.00

20.0

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25.0

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90

130

1: UNa conc 2: ECNa conc 3: ECFV 4: ICFV 5: Urine flow

1

11 1 1

2

2 2 2 2

3

3 3 3 3

44 4 4 4

5

5

5 5 5

Hours

ECNa concentration on their own with reasonable effective-ness. On the other hand, if both systems are blocked simul-taneously, the ECNa concentration changes tremendously,as expected by empirical evidence (see Figure 4.10).In the third experiment, the effect of ALD (Aldosterone)

feedback on ECNa concentration is sought, so the experi-ment is repeated by blocking the ALD feedback (see Fig-ure 4.11). It is seen that ECNa concentration is almostequally well controlled with or without the ALD feedbackmechanism, which demonstrates that the ECNa concentra-tion is mainly regulated by the ADH-thirst system, and theALD system has little role in this regulation.The general results above corroborate the prevailing

theory for the Na homeostasis, stating that simultaneouschanges in body sodium (and potassium) are accompanied


Figure 4.9. Sensitivity of EC sodium concentration to different daily sodium intakes.

0.00 12.00 24.00 36.00 48.00

Hours

143.50

146.50

ECNa conc: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 -

140.50

by osmotically adequate changes in TBW, and that osmo-control effectively adjusts TBW to its major substances Na(and K). Recently, a new concept of Na homeostasis wasput forward by Titze et al. (2003), claiming that during Naretention, large portions of Na (up to 75%) are stored inan osmotically inactive form. In contrast, a recent study bySeeliger et al. (2005) does not support this notion, arguingthat there is no positive proof for this Na storage because Kbalances were not assessed, and response to changes in Na

Figure 4.10. Effects of changes in sodium intake on EC sodium concentration (a) under normal conditions (solid line)and (b) after the ADH-thirst feedback has been blocked (dashed line). Empirical data (part a) from Guytonand Hall (2000) versus simulation results (part b).

100

110

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200

0.2 0.4 0.6 0.8 1.31.0 1.6 1.9 2.3

Normal

ADH-thirstblocked

ADH-thirstsystemblocked

Sodium intake (times normal)

Sodium intake (mEq/day)

Pla

sma

sodi

um c

once

ntra

tion

(mE

q/L)

152

148

144

140

1360 30 60 90 120 150 180

Normal

(a) (b)


intake varies among species. Both our model and the recentstudy by Seeliger et al. (2005) reveal that further studies areneeded to explore the subtleties of body sodium dynamics,especially by including the body potassium dynamics.

4.4. Representing Diseases (Dysnatremia) andTreatment Options

The model discussed above represents the fundamentalfeedback structures of body water and osmolality regulation


Figure 4.11. Effects of changes in sodium intake on EC sodium concentration (a) under normal conditions (solid line)and (b) after the ALD feedback has been blocked (dashed line). Empirical data (part a) from Guyton andHall (2000) versus simulation results (part b).

130

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110

1000 30 60 90 120 150 180 210 0.3 0.5 0.8 1.0 1.2 1.5 2.0 2.5 3.0

Sodium intake (times normal)

Normal

Sodium intake (mEq/litre)

Pla

sma

sodi

um c

once

ntra

tion

(mE

q/lit

re)

ALDblockedNormal

Aldosterone system blocked

(a) (b)


in a healthy person. Because the ultimate goal would be toprovide assistance in the diagnosis and treatment of relateddiseases, the next step is to modify the model so as to repli-cate some common body water-sodium regulation disordersand to test alternative treatments. To this end, structures aremodified or new structures are added to the original modelto represent disease physiology and the treatment options,and some new variables are added for disease-related out-put measures.

4.4.1. Representation of Hypernatremia (DiabetesInsipidus as a Common Type). Increased levels of ECNaconcentration or hypernatremia is typically seen when thereis excess loss of water (Haslett et al. 2002). DiabetesInsipidus (DI) is the most common type of pathologic condi-tion that is associated with hypernatremia. Insipidus means“tasteless,” therefore the term “Diabetes Insipidus” distin-guishes excessive urine flow caused by inability to con-serve water, from Diabetes Mellitus in which urine flow isenhanced due to excessive glucose excretion. In DI, defi-ciencies of ADH lead to the production of large amountsof dilute urine, which may reach up to 20–30 liters a dayin severe cases. More commonly, however, urine volume ismoderately increased (2.5 to 6 L/day). Consequently, theperson becomes dehydrated.To simulate an extreme case of DI, the pool capacity of

ADH is decreased by 90% (Figure 4.12). It is seen thatthe TBW can no longer be conserved, and the ECNa con-centration can only be kept at an elevated level (Verbalis2003). On the other hand, the blood pressure is kept con-stant at its normal level of 100 mmHg. The urine flow andhence drinking—to replace the loss—are highly elevated(drinking becomes extremely frequent in the discrete drink-ing version of the model). The urine concentration is verylow, as expected. The daily water turnover of this patient is

about 11 liters, which is far greater than the normal valueof 2–3 liters.

4.4.2. Representation of Hyponatremia (SIADH as aCommon Type). SIADH is the most common cause ofhyponatremia (38%). Both the thirst function and ADHaction have to be deregulated to bring about hypoosmolalitythat occurs in SIADH. Therefore, first the set level ofthe ADH concentration is increased, and then the thirstfunction of the potential patient is modified in the model.Accordingly, the patient has an elevated normal fluid intakeand she cannot suppress her water intake as a resultof hypoosmolality. The equations for the urine sodium con-centration are also modified to include the effects of apossible administration of the Aquaretic and the Diureticdrugs. The equation for drinking is modified so that a mildor severe water restriction can be imposed on the patientas a treatment option. (The terms “mild” and “severe” cor-respond to daily water intakes of 1,700 and 800 ml/day,respectively.)The modified model is then used to demonstrate the

appearance of hyponatremia in the SIADH. To develophyponatremia, both ADH and the thirst functions have tobe deregulated. This fact is demonstrated by simulating themodified model first by increasing the ADH level withoutchanging the thirst function, and second, by disturbing thethirst function without changing the ADH function. It isseen that the resulting decrease in ECNaConc is very small.However, when both ADH and the thirst function are dereg-ulated, there is no mechanism that can preserve the levelof the body water and the ECNaConc. As an example, thedynamics of the emergence of hyponatremia is illustratedin Figure 4.13. In five days, the ECNaConc of the patientfalls to 120 mEq/L, and the TBW is increased by about fiveliters. The final values of this simulation are used for the


Figure 4.12. Dynamics of the key variables in Diabetes Insipidus where ADH is incapacitated.

0.00 24.00 72.00 96.00 120.00Hours

39,050

39,525

40,000

142.00

144.75

147.50

95

100

105

25

78

130

50

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350

1: TBW 2: ECNa conc 3: MAP 4: UNa conc 5: Drinking

1

1

1 1 12

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22 2

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33 3

4

4 4 4 4

5

5

5 5 5

48.00

initialization of the interactive game, where a patient withacute hyponatremia is assumed to be admitted to a hospital.

4.4.3. Treatment Sector for Hyponatremia. An im-portant intended application of the model and its gameversion is to test the effectiveness of different treatmentoptions for specific diseases. In particular, we focus on thetreatment of acute hyponatremia. The simulated patient isassumed to have an ECNa concentration of 120 mEq/L andan excess body water of about 5 L. The treatment goal

Figure 4.13. Appearance of hyponatremia when both ADH and the thirst functions are blocked.

0.00 24.00 48.00 72.00 96.00 120.00

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2,200

115.0

130.0

145.0

15

15

15

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1: TBW 2: ECNa 3: ECNa conc 4: ECFV 5: MAP

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1

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3

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Hours

is to increase and sustain the ECNa concentration (ECNa-Conc) at its normal level, which is about 140 mEq/L. Atthe same time, the total body water should be decreased toits normal value (of 40 liters) and so should the EC and theIC water volumes. The new treatment sector is composedof three subsectors, two of which are almost identical, i.e.,Diuretic and Aquaretic (or ADH-Antagonist) drug sectors.These two sectors represent the most commonly used drugsfor treatment of hyponatremia (Yamamura et al. 1993, Saitoet al. 1996, Shafiee et al. 2003). The drug metabolization


structure used in isee Systems (1997) is assumed to beappropriate for the scope of this research. The third subsec-tor, i.e., intravenous fluid infusion, constitutes another stan-dard therapy for treating severe hyponatremia. The threemost commonly used types are represented in the model:hypertonic, isotonic, and hypotonic fluids, which are clas-sified according to their sodium content. These treatmentoptions are illustrated below in the interactive game sec-tion. (Also see the online supplement.)

5. The Interactive Dynamic Simulator(BWATERGAME)

5.1. Game Description

Finally, an interactive game version of the model is built,whereby players can diagnose hyponatremia and test varioustreatment strategies on a virtual patient. The player plays thepart of a physician who is trying to treat an acute hypona-tremic patient by weighing the risks of hyponatremia itselfand those associated with rapid correction of the disease.The primary goal is to increase and sustain the ECNa con-centration �ECNaConc� at its normal level, which is about140 mEq/L. Simultaneously, the total body water volume,as well as the EC and the IC water volumes, should bedecreased to their normal levels. The challenge is to achievethese goals in balance, keeping in mind that rapid correctionof severe hyponatremia can cause brain edema. The totalduration of the game is 160 hours, or 20 decision rounds.The player should revise her decisions at each step, by mak-ing use of the provided analysis tools. The treatment optionsavailable to the player are: Dose Diuretic, Dose Aquaretic(ADH-Antagonist), Isotonic Saline, Hypotonic Saline, andHypertonic Saline (see the game control panel in the onlinesupplement). Moreover, the player can change some of thegame settings or impose water restriction to the patient byvarying the scenario. A more detailed description of thegame can be found in the user manual (see the online sup-plement and Karanfil 2005, 2006).

Figure 5.1. Saline infusion (seen as step functions) and drug dose decisions (seen in spikes) for a representative player.

0.00

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750

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0

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750

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2

1 1 1 1

2

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22

3 3 3 3

2: Isotonic saline1: Dose aquaretic 1: Dose diuretic 2: Hypertonic saline 3: Hypotonic saline

40.00Hours

80.00 120.00 160.00 0.00 40.00Hours

80.00 120.00 160.00

5.2. Results of BWATERGAME by Test Players

The game was tested by graduate students of the IndustrialEngineering Department of Bogaziçi University, Istanbul.Each subject played the game several times and applieddifferent strategies in their trials. The graphs in Figures 5.1–5.4 represent the dynamics of a few key measures obtainedfrom a typical representative player. Figures 5.1 and 5.2display the dynamics of the player’s saline infusion anddrug dose decisions, and Total body water, ECNa concen-tration, Urine Na concentration, and ECNa as outputs.As can be seen in the figures, the representative player

initially was unable to prevent the decline of the EC sodiumconcentration to levels below 115 mEq/L, but then he suc-ceeded to increase it to mildly hyponatremic levels towardthe end of the game. He used a combination of Aquaret-ics and Diuretics to increase urine flow via a decreasedurine sodium concentration, and also applied a combina-tion of hypertonic and isotonic saline during his trial. Totalbody water increased by 1.5 L in the initial phase, andthen it decreased. At the end of the game, the simulatedpatient still has about 4 L of excess water. The player firstwrongly chose to give hypertonic solution without drugs,but this only resulted in a fall in EC sodium concentrationand a rise in blood pressure. Hypertonic saline combinedwith urine flow stimulating drugs later caused an elevatedsodium balance and negative water balance.Figures 5.3 and 5.4 on the other hand depict the game

results of a player with a reasonably successful treat-ment strategy. The successful player used a combina-tion of aquaretics and isotonic saline. In contrast to therepresentative player, he was able to reduce the urinary Naconcentration to its normal levels by using the aquareticsalone, instead of a combination of diuretics and aquaret-ics that blunts the kidney’s response. He was also able toreplenish the sodium deficits. At the end of the game, hedecreased the TBW to 42.2 liters, and the ECNa concen-tration rose to 133 mEq/L.There is no single correct set of treatment decisions, as

long as certain critical balances are simultaneously takeninto account. (As mentioned before, the correction rate is


Figure 5.2. Dynamics of total body water, ECNa concentration (seen in spikes), UNa concentration (seen in spikes),and ECNa for a representative player.

0.00

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3: UrinaryNa conc

4: Normal UNaconc

32.00 64.00 96.00

Hours128.00 160.00 0.00 32.00 64.00 96.00

Hours128.00 160.00

Figure 5.3. Saline infusion (seen as step functions) and drug dose decisions (seen in spikes) for a player with a successfulstrategy.

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4: Hypotonicsaline

1 1 1 12 2 2 23 3 3 34 4 4 4

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160.00 0.00 40.00 80.00 120.00

Hours160.00

Figure 5.4. Dynamics of total body water, ECNa concentration (seen in spikes), UNa concentration (seen in spikes),and ECNa for a player with a successful strategy.

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33 3

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1: ExtracellularNa conc

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1: ExtracellularNa

2: NormalECNa

3: UrinaryNa conc

4: NormalUNa conc

32.00 64.00

Hours96.00 128.00 160.00 0.00 32.00 64.00

Hours96.00 128.00 160.00


also a vital concern while managing the hyponatremia ofthe patient.) The two goals of the treatment should beconsidered concurrently: attaining a negative water bal-ance and replenishment of the sodium deficits. Diureticsmay be useful in correcting the excess body water, butshould be supported by high amounts of sodium. So, theplayers that used Diuretics instead of Aquaretics had toadminister high amounts of saline. While Aquaretics maydecrease the urine sodium concentration to levels belowits normal, Diuretics can only blunt the urinary concentra-tion process, so they can decrease the UNa concentrationat most to its normal level. Generally, players administeredDiuretics and Aquaretics together, and Diuretics reducedthe effectiveness of Aquaretics in those trials. This demon-strates that Diuretics should not be administered in severecases of hyponatremia.Another important point to note is the EC sodium level

of the patient. Because the sodium-preserving systems areintact in an SIADH patient, the ECNa content is preservedat a lower steady-state value. However, sodium depletionmay worsen the condition of the patient due to decreasedsodium and decreased urine flow. SIADH patients typi-cally have a normal or slightly elevated mean arterial pres-sure level, and this level should be closely monitored. Lowarterial pressure levels may inhibit the urine flow increasingstrategies, and a high level of arterial pressure is undesir-able for obvious reasons.The game results so far demonstrate that the interactive

simulator (BWATERGAME) can be a useful experimentalplatform to study the subtleties involved in the adminis-tration of different pharmacological interventions (also seeKaranfil 2005, 2006). Our current research involves moreextensive testing of the simulator and statistical analysis ofthe experimental results.

6. Conclusions and Further ResearchThe goal of this research is to model the normal andabnormal physiology of the body water and sodium reg-ulation in humans and to test treatment strategies fora particular body fluid disorder, namely, water intoxica-tion/hyponatremia. For this purpose, first a system dynam-ics model is built representing the dynamics of the bodywater and sodium balance for a normal individual. Then,this model is extended to generate common disorders ofbody water regulation (both hypernatremia and hypona-tremia) and to explore effective treatment strategies. Com-parisons with experimental and field data show that themodel adequately reproduces typical dynamics of the bodyfluid variables in normal and pathological states. Sensitiv-ity results also agree with high resilience known to existin the human body as a feedback control system. Based onthe extended model, a game version is finally constructedwhereby players can interactively treat a virtual patient withacute hyponatremia. The game is used as an experimen-tal platform to test the effects of a typical set of treatmentoptions on a simulated patient.

The model demonstrates that ADH (Antidiuretic Hor-mone) is extremely important for the control of sodiumconcentration, yet it has a relatively mild effect on the con-trol of blood volume/pressure. The modified model for thedevelopment of hyponatremia reproduces all the cardinalfeatures of the SIADH (Syndrome of Inappropriate Antid-iuretic Hormone Secretion). Blocking of the ADH-thirstsystem first causes an increase in the body fluids, but thentransient sodium loss is promoted. As a result of dilution,ECNa concentration falls drastically, but the arterial pres-sure is only slightly elevated. Moreover, urine is still highlyconcentrated due to the absence of compensating feedbackbetween the ECNa concentration and the ADH.The interactive simulation game (BWATERGAME)

yields meaningful results for various treatment options.Game results reveal that an effective correction of theSIADH can only be attained if a negative water balancecan be maintained. Replacing the sodium deficits alone isworthless because, following a sodium intake, blood pres-sure conserving mechanisms cause an increased sodiumexcretion rate. It is demonstrated that Aquaretics (thatincrease the urine flow) are the most effective treatment,together with slow replenishment of body sodium stocksby graded doses of saline infusion. However, they shouldbe administered carefully to prevent an overcorrection.In conclusion, the model and the interactive game ver-

sion constitute an experimental laboratory for systemictherapy of hyponatremia. They can be used as a researchand teaching tool on renal physiology, on the importantdifferentiation between the concepts of “sodium content”and “sodium concentration,” between their equilibrium anddynamics, and related disorders.There are several avenues in which this research can

be expanded. We are already working on more extensivegaming experiments by players with different backgrounds,carried out with a suitable design of experiments and sub-sequent statistical analysis of results. Another research stepis modifying the current game model for the treatmentof severe hyponatremia in an intensive care unit setting,by changing the initial conditions of the modified modeland the treatment options.Hyponatremia can occur with many electrolyte imbal-

ances (other than sodium), hypokalemia (potassium deficit)being the most common electrolyte disorder. Another sub-stance ignored in our model is the urea. We have representedthe urine osmolality by its sodium chloride concentrationonly; however, in reality urea also contributes significantlyto the urine osmolality when the kidney forms a maximallyconcentrated urine (Guyton and Hall 2000). Modeling of theinteractions of the treatment options of hyponatremia withpotassium and urea dynamics may reveal a broader range ofpossible physiological phenomena.

7. Electronic CompanionAn electronic companion to this paper is available as partof the online version that can be found at http://or.journal.informs.org/.


Appendix. AbbreviationsADH Antidiuretic HormoneALD AldosteroneANG AngiotensinANH Atrial Natriuretic HormoneBV Blood volumeDI Diabetes InsipidusEC Extracellular

ECFV Extracellular fluid volumeECNa Extracellular sodium

ECOsm Extracellular osmolalityGFR Glomerular Filtration RateIC Intracellular

ICFV Intracellular fluid volumeICOsm Intracellular osmolality

K PotassiumL Liter

MAP Mean Arterial PressureNa SodiumPV Plasma volume

RAAS Renin-Angiotensin-Aldosterone SystemSIADH Syndrome of Inappropriate ADH SecretionTBW Total body water

U Urine (or Urinary)UNa Urinary sodium

UOsm Urine osmolalityconc concentrationeff effect

mEq milliequivalents

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