558
FLUID THERAPY IN ACUTE LARGE AREA BURNS:
A SYSTEM DYNAMICS ANALYSIS
Bush, James W. [1], Schneider, Alan M. [2], Wachtel, Thomas L. [3],
and Brimm, John E, (4]
Departments of Community and Family Medicine [1], Applied
Mechanics and Engineering Sciences [2], Surgery [3], and Pathology [4]
University of California, San Diego, La Jolla, CA 92093
Running Head: Burn Fluid Therapy
Key Words: computer simulation, mathematical models, System Dynamics,
systems science, acute burns, extracellular water, renal output, homeo-
stasis, dehydration, Brooke formula, control theory, fluid balance, shock,
resuscitation, blood volume, hemoconcentration, plasma, electrolytes
To be presented at the International Conference on System Dynamics
Newton, Massachusetts
duly 1983
Acknowledgements: We wish to thank Dr. Robert Zeldin for helpful
discussions during the early model formulation, Professors Ed
Roberts, Jay Forrester, and the Sloan School of Management, for
their hospitalilty and’ support during the first author's sabbati-
cal at MIT, the Dean's Office, school of Medicine, University of
California, San Diego, for initial financial support, Rosemary
Buerger, Jane Chamberlin and Suzanne Burns for secretarial assis-
tance, Ester McConnell and Michelle Harden for research and li+
brary assistance, Ray Madachy and David Whiteman for computer
programming, and the UCSD Computer Center for processor time and
software support.
ABSTRACT
A preliminary mathematical model of fluid dynamics in acute
large area burns presently incorporates plasma water, urine out-
put, burn water loss, insensible losses via the non-burned skin,
lungs, and G-I tract, as well as inputs of maintenance water and
theraputic (Brooke Formula) fluids. The model is an initial step
in a longer-term project to identify the pathogenetic mechanisms
that control fluid shifts and to evaluate the effects of crystal-
loid (sodium ion), colloid (albumin), and other guidelines for
fluid resuscitation. The model is initialized in homeodynamic
equilibrium for a standard 70 KG person, and gives reasonable,
realistic responses to a wide range of parameter variations (body
sizes, burn wound loss factors), step functions (burn size,
discontinuation of maintenance water), and rates of therapeutic
fluid administration, given its present structure. The addition
of burn and nonburn interstitial and intracellular spaces and
their constituents (water, sodium, albumin and potassium) will:
1) permit validation against a wide body of clinical and experi-~
mental data, 2) suggest refinements of current resuscitation
guidelines, 3) suggest more incisive research on pathogenetic
mechanisms and treatment modalities, and 4) permit comparison of
System Dynamics with alternative modeling and simulation
approaches.
FLUID THERAPY IN ACUTE LARGE AREA BURNS:
A SYSTEM DYNAMICS ANALYSIS
INTRODUCTION (1.0)
BACKGROUND (1.1)
System Dynamics has been applied to several biomedical prob-
lems in the past [1-5]. In addition, a rapidly increasing number
of standard engineering and control theory simulations are being
constructed for pathophysiological processes [6-20].
Because of the large volume of clinical and experimental
data available, and because of the short time constants in phy-
siological as compared to corporate, social, and economic sys~
tems, studies of pathophysiology with System Dynamics have the
methodological merit of affording a direct contrast with alterna-
tive approaches to model formulation, analysis, use, and valida-
tion.
Most physiological models have been formulated help identify
physiological organ systems, rather than to to precisely charac-
terize pathological states and improve their clinical management.
Many have been done as illustrative teaching exercises.
DYNAMIC PROBLEM (1.2)
Fluid therapy in acute burns offers an opportunity to study
a relatively frequent clinical problem of short duration involv-
559
ing several organ systems that can be used to compare System
Dynamics with more orthodox analyses. The problem has received
more quantitative attention than many clinical medical problems
[21-34], but only limited attention from control theorists. That
effort, since abandoned, tried to use an empirically determined
canine transfer function to guide microprocessor control of infu-
sion [35].
Patients burned over a large portion of their body immedi-
ately begin to lose large amounts of plasma water, protein,
sodium and potassium from the wound. This is initially replen-
ished from the interstitial fluid that occupies the space between
the cells of the body, especially in the muscles and skin.
As the breakdown products from the burn wound circulate
throughout the vascular system, a generalized inflammatory
response is initiated that increases the permeability of capil-
lary membrane throughout most of the normal tissues so that the
circulating plasma protein (albumin) escapes into the intersti-
tial space.
Because proteins maintain the intravascular osmotic pres~
sure, their loss into the interstitial fluid slows or even halts
the replenishment of the circulating plasma volume. This loss of
circulating blood volume produces hypovolemic shock, depresses
cardiac and kidney output, decreases tissue perfusion, increases
acidosis, and eventually kills the patients.
The treatment involves replacing the continuing losses of
560
water, sodium (crystalloid), and albumin (colloid), at a rate
that will maintain urine output and fill up the interstitial
Space so the blood volume can also be maintained.
A very real danger exists, however, especially in older and
younger patients, that an overshoot will occur in the fluid loads
given and the patient will die from cardiac failure or pulmonary
edema (fluid in the lungs). Several days postburn, with
decreases in various stress hormones, the kidneys begin excreting
voluminous urine output until the stored water is pulled down to
near normal levels.
Discovery of the dramatic effects of fluid therapy during
and immediately following the Korean War was a major breakthrough
in burn resuscitation. The use and optimal rates of administra-
tion of the different components of the fluids has continued to
be a source of controversy, however, despite three decades of
progressive understanding of the basic physiology based on animal
as well as clinical research.
The issue concerning colloid is whether (expensive) plasma
proteins are of value in therapy, or whether they are useless in
fluid management because of the 26 to 30 hour increase in capil-
lary permeability and perhaps eventually harmful because they
increase the viscosity of the interstitial gel and retard healing
[36].
This problem seemed worthy of attention from System Dynam=
ics.
METHODS (2.0)
Our methods include the construction of the model, analysis
of the responses to step functions, sensitivity analyses of its
parameters, and analyses of responses to standard treatments.
Comparisons with known relationships, experimental data, and
responses to treatment will be made at several points.
MODEL CONSTRUCTION (2.1)
To initialize the model in equilibrium, we adopt the parame~
ters of a 70KG person -- a standard reference case in physiology,
Our model represents the forces implicit in normal physiology. A
burn is then imposed on the patient, followed by alternative
treatments.
The model is generalized to persons of all sizes and shapes
by defining a weight ratio WGHTR to the standard person.
Although linear, this formula refines the usual clinical rules
where adult averages are used rather than precise calculations.
Using the patient's known height and weight, standard formu-
las estimate the body surface area, blood volume, red cell mass,
and plasma water volume. Rate equations are usually related
either to body surface area or to lean body mass, which is more
closely related to height than to recorded weight.
In equilibrium, maintenance water comes in by mouth or by
vein IVWM, and escapes via insensible losses INS, which sums
losses from separate rates for the skin, lungs, and the
gastrointestinal tract. These rates are affected only by the
level of plasma water itself.
Water is also lost by urinary excretion UX, which responds
to the plasma water through the blood volume consisting of a
fixed volume of red cells RC and the plasma. Variations in the
blood volume BV presently reflect only changes in plasma water.
Urine excretion at any time is equivalent to the normal urine
exeretion UXN modified by the current level of plasma water PW by
a multiplier UMBV that summarizes the renal response to blood
volume.
The rate of water loss via the burn wound BWL is set as a
multiplier BWLM of the normal unit skin water loss SWLFN. This
rate is further modified by the size of the burn area BA, the
plasma water ratio PWR, and a control variable BURN for the pres-
ence or absence of a burn.
Another rate represents maintenance water IVWM controlled
exogenously at water cutoff and turnon times MWCOTM and MWTOTM,
An "accounting" level IVWIT sums the total water given from all
sources after the time of the burn BRNTM, but does not interact
in any feedback processes.
Normal flow rates at equilibrium for the 70 KG person are
transformed to proportional flow rates for persons of other
weights. Equilibrium flow rates of 1500 ML per day for normal
urinary excretion UXN, 500 ML per day for total skin water loss
at SWLTQ, and 500 ML per day for lung and GI loss LWL all combine
561
to produce a maintenance water requirement IVWM of 2500 ML per
day for the standard person.
These equilibrium values generate average hourly flow rates
for urine excretion UX of 63 ML per hour, lung and GI losses LWL
of 21 ML per hour, and normal skin water losses SWL of 21 ML per
hour. The blood volume ratio BVR and the plasma water ratio PWR
relate the current values to the equilibrium values for persons
of that height and weight.
Initial inputs to the model are of three forms: 1) charac-
teristics of the patient such as height HTIN, weight WIN, and
burn size BSAB, 2) constants that cannot be derived from the
equilibrium conditions, such as the burn water loss multiplier
BWLM, and 3) settings for control switches that represent water
inputs, the time of the burn, and the time of treatment.
TEST FUNCTIONS (2.2)
The preliminary analyses reported here contrast several
aspects of different treatments, as follows:
1) Continuation in equilibrium vs. discontinuation of mainte-
nance water in the unburned person, a step representing
total fluid deprivation.
2) Continuation vs. discontinuation of maintenance water in the
burned patient, testing the model's emulation of no treat-
ment vs. low-level, inadequate treatment, and
3) The institution of the Brooke formula at 4 and at 8 hours
respectively, with no fluid from burn time BRNTM until
treatment time RXTM.
These fundamental fluid variations are emulated in the stan-
dard 70 KG person with 10, 40, and 80% burns. The present model
permits us to examine the response of the renal-cardiovascular
complex to a burn without the physiological (but clinically con-
founding) effects of the interstitial "third space" reservoir.
SENSITIVITY ANALYSIS (2.3)
Minimum tests for sensitivity include high and low values
for each important factor around a baseline case. The possible
combinations of parameter values grow exponentially with the
number of variables being studied, as well as the number of lev-
els taken of each variable, so a comprehensive analysis quickly
becomes intractable,
One shortcut is "extreme" or "worst case" analysis, in which
all the extreme (high or low) values are taken together simul-
taneously. If the model behaves appropriately at such extremes,
then the assumption of appropriate behavior at intermediate
values of the system variables is much more strongly assured.
In the burn case, for example, we can combine all the fac-
tors with bad prognoses currently in the model, e.g. a small
patient, a big burn, a large coefficient for burn water loss, and
delayed treatment as a "worst case". If the model produces good
562
outcomes, or bad outcomes too quickly, then the modelhas been
falsified in some respect and we must refine the previous effort.
TREATMENT SELECTION (2.4)
The appropriate clinical response to complex problems like
fluid therapy is a sophisticated blend of multiple rules, based
on qualitative knowledge of the underlying process, but most
heavily on the responses of previously observed and reported
patients.
All our decision rules can be tested individually, in combi-
nation with each other, and with different conditions of the
patient (settings of the uncontrollable variables), This permits
us to evaluate the therapeutic response, unanticipated side
effects, and most importantly, appropriate timing to avoid iatro-
genic (physician induced) undershoots and overshoots.
Prescribed water RXW is represented by a level that is
filled with the fluid calculated for the first forty-eight hours.
The level of treatment water RXW is presently prescribed by the
BROOKE formula calculated from the normal weight WIN and body
surface area burned BSAB.
Its infusion RXW2IV is controlled by the amount of
prescribed water remaining and the IV treatment water time
IVRXWT, The present model does not alter the prescribed input by
any information on the patient's state.
oe
In sensitivity analysis we adopt the model structure and
parameter values that best reproduce known behavior. In treat=
ment selection, we choose those rules or treatment variable coef-
ficients that produce the closest approximation of our desired
outcomes, i-e., survival, restored homeostasis, and improved
quality of life.
Present burn treatment formulas do not constitute rules of
this form. They represent, instead, the aggregated results of
the hour-to-hour feedback from hundreds of previous patients. In
complex systems, this well-formulated experience aids in tracking
the patient by anticipating the course of therapy, and permits
the derivation of more sensitive and refined treatment rules.
This derivation of treatment rules involves making explicit
the previously implicit moment-to-moment guides used for online
therapy. In medicine, where data on treated patients are more
common than data on untreated, known responses to alternative
treatments also provide additional tests of validity.
Practically speaking, truly optimal therapies do not exist.
Multiple therapeutic approaches may be equivalently good (or
bad), and the compensations induced by the underlying physiologi-
cal feedback structure may cancel out the advantage of one
therapy over an alternative. Whether this indeterminacy accounts
for enduring dilemmas about colloid vs. crystalloid, or hypotonic
vs. hypertonic sodium solutions, remains to be investigated.
Although intuition and formal analysis can eliminate some
563
2
treatment combinations from consideration, we must eventually
resort to strategies such as extreme case analysis to extract
general guidelines. We plan to formulate and evaluate sets of
feedback rules without, as well as with, existing formulas.
The preliminary model reported here includes the Brooke for-
mula without regard to information about the patient's state;
this open-loop analysis although clinically unrealistic -- is
a helpful concept in model identification, As with all uncou-
pling of system structure, analysis of the resulting behavior
frequently clarifies the effects in the patient where the system
is actually coupled.
564
13
RESULTS (3.0)
The following sections present the salient features of the
model and its response to several test functions. Note that the
time scale is compressed after TIME = 30 to'preserve detail ini-
tially while displaying longer term outcomes on the same graph.
The results of the computations for different size persons are
generally reasonable but are not tabulated for this paper.
Results of Case 1: Long-Term Water Deprivation
An initial test of the validity of the model is a negative
step function that drops maintenance water IVWM from equilibrium
levels to zero with no subsequent rise. The patient has no burn
and receives no treatment. The plasma water PW falls gradually
over the ensuing 48 hours, the plasma water ratio PWR reaching
approximately 50% of its normal value at 30 hours.
By that time, urine excretion UX has declined to less than
10 ML per hour (and normal skin water loss SWL has also declined
markedly) with the hematocrit HCT rising to .57. These trends
continue to almost universally fatal levels by about four days,
which approximates our understanding of the clinical situation.
Short-Term (30 Hour) Water Deprivation
Results of Case
Case 2 also discontinues maintenance water IVWM at time
zero, but restores IVWM at 30 hours with no burn and no other
treatment. The plasma water PW is lost initially at the same
rate as in the previous case.
When maintenance water IVWM is restored (perhaps by mouth)
at 30 hours, however, the multiplier for the effects of blood
volume UMBV continues to reflect the low plasma water volume and
inhibits urinary excretion, The plasma water PW, and its associ-
ated auxiliaries and rates, such as hematocrit HCT, urinary out-
put UX, skin water loss SWL, and blood volume BV, all return
almost to normal over the next 24 hours, with virtually complete
equilibration by 60 hours.
This case demonstrates the smooth and appropriate operation
of the renal excretion multiplier UMBV, which summarizes the
action of multiple hydrostatic, osmotic, and hormonal fluid
retention and release mechanisms, without the addition of thera-
peutic fluids,
Results of Case 3: 40% Burn with No Treatment
With all the parameters set for the same equilibrium, a burn
at time zero is simulated by a step in the burn water loss multi-
plier BWLM to 20 times the normal skin water loss, where it
remains for the duration of the run. This "parameter excitation"
activates the burn water loss rate BWR, which is set at the
outset for a 40% burn.
The water loss from the burn BWL therefore steps to approxi-
mately 100 ML per hour initially and then declines gradually as
plasma water PW decreases. The sensitivity of the model to that
function is examined below.
The plasma water ratio reaches 50% of its normal value in
about 12 hours; which corresponds closely to the clinical course
of the patients. By that time, urine excretion UX has declined
below 10 ML per hour and the hematocrit has risen to 55.
Skin, lung and GI water loss, along with the blood volume,
fall accordingly. If mortality were 50% with a 50% loss of
plasma, then at least half the patients would die before 12 hours
and almost all would die within 24.
Results of Case 4 (Base): 40% Burn with BROOKE Treatment
This case the baseline for all further tests -- begins
with all the previous equilibrium conditions, including the
changes induced by a 40% body surface area burn BSAB. In addi-
tion, treatment is initiated at treatment time RXTM 4 hours
postburn by the prescription RXW of the Brooke formula for 48
hours. This is administered at an initially high but decreasing
rate RXW2IV corresponding to the formula and to, common clinical
practice.
The Brooke formula includes the maintenance water to be
administered over the 48-hour postburn period. The plots demon=
strate the initially declining plasma water PW, urine exeretion
UX, and burn water loss BWL, and the rising hematocrit HCT, just
as in the untreated Case 3.
In this instance, however, intravenous water RXW2IV is given
rapidly beginning at 4 hours postburn (RXTM = 4). The plasma
water, urine output, and blood volume respond immediately with a
565
substantial overshoot of equilibrium in all three variables, with
the plasma water ratio PWR rising to almost 1.6 times normal.
This overshoot -- an unphysiologic response that is not usu-
ally observed clinically reflects the unusually high IV infu-
sion rate and especially the absence of an interstitial space (in
the present model) to absorb the water.
Despite the overshoot, the continuing burn water loss BWL
pulls the plasma water PW and the blood volume BV back to near=
equilibrium levels at 34 hours. The burn water loss BWL continues
until the patient again becomes severely dehydrated by about 48
hours. The ensuing course up to 5 days postburn demonstrates
that restoring maintenance water IVWM alone, after exhausting the
Brooke formula, is insufficient to replace the ongoing burn water
loss BWL.
In clinical practice, the continuing losses would usually be
met by the oral intake of the patient, governed by thirst, which
is not represented in the current model. Given the specified
structure, however, the response is realistic.
Results of Cases 5, 6: Sensitivity Analysis of Burn Water Loss
Multiplier BWLM
Cases 5 and 6 show the sensitivity of different values of
the burn water loss multiplier (BWLM = 5 and 20). Despite previ-
ous measurements [37,38], the precise value of this factor for
the water loss per unit area is uncertain, and measurement
results have varied over a wide range. These sensitivity tests
are both in a 70 KG person with the 40% ("standard") large area
burn.
For BWLM = 5, dehydration and hemoconcentration do not
develop as rapidly. Because the high volumé of the Brooke for-
mula is computed in exactly the same way, however, the plasma
water ratio PWR rises to even higher, more unphysiologic levels
than in base case 4, Similarly, urine excretion UX rises much
higher, and the hematocrit falls slightly lower than in the
reference case.
Water loss from the wound BWL also lags substantially behind
the reference case, but still varies by a factor of 2, reflecting
hydrostatic pressure from the plasma water level PW. As in the
base case, the combined water losses gradually exceed the formula
input and the patient becomes dehydrated again before maintenance
water IVWM is restored at 48 hours. A new equilibrium is then
established with the plasma water ratio at a slightly lower level
(PWR = .86) than in the base case and with a decreased but clini-
cally sufficient urine excretion (UX = 41 ML/HR).
Case 6 is identical to the base Case 4 and Case 5 except for
the increase of the burn water loss multipler BWLM to 20 times
the normal skin water loss SWLFN. As expected, it shows a much
higher rate of burn water loss over the 48 hour resuscitation
period,
The burn wound still demonstrates markedly varying hour to
hour water loss, however, even though the burn water loss multi-
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18
plier BWLM is constant for a given burn. The marked variation
directly reflects the changing pressure from plasma water volume
PW as the patient first becomes dehydrated, then overinfused,
then dehydrated again.
The plots show a new equilibrium with plasma water at
approximately 50% of normal, which is only marginally compatible
with life. In the clinical situation, the patient would probably
be on oral fluids ingesting much larger than maintenance volumes,
or such volumes would be administered intravenously. Revisions
of the model will correct these deficiencies.
These two runs demonstrate fundamentally the same pattern of
dehydration, overcompensation, decline to below maintenance, and
restoration to a new (perhaps unphysiologic) equilibrium.
Although the burn water loss multiplier BWLM was varied by a fac-
tor of 4, the change in the pattern of the model behavior was
modest.
Results of Cases 7, 8: Sensitivity Analysis for Burn Size BSAB
Cases 7 and 8 display the model response to small and
extremely large body surface area burns (BSAB = .1 and .8). The
burn water loss multiplier BWLM is reset at 10 times normal skin
loss, as in the base case.
In Case 7, with a body surface area burn BSAB of only 10%,
the burn water loss BWL is much lower than in previous cases.
Other curves show the same fundamental pattern but with much nar-
rower excursions. The plasma water rises only slightly above
567
19
equilibrium, since the Brooke formula prescribes a lower volume
for a smaller burn. Plasma water PW again descends to dehydra-
tion levels after 30 hours, and recovers only to a diminished
equilibrium, since wound water losses continue even after mainte-
nance water is restored at 48 hours (MWTOTM = 48).
With an 80% burn (Case 8), the initial dehydration (and
hemoconcentration) progress more rapidly and then respond more
dramatically to the much larger volumes of prescribed fluid RXW.
Despite the huge volumes of fluid -- over 18 liters -- the plasma
water ratio PWR again falls below. equilibrium by 36 hours.
Because of continuing high burn water losses, the resumption
of maintenance water IVWM brings the plasma water up to only 1/3
of its initial equilibrium level. This is insufficient to sus-
tain life.
Despite an eightfold variation in the burn size BSAB and a
fourfold variation in the initial volumes of prescribed fluid
RXW, the same basic response pattern recurs. The feedback
between plasma water volume PW and the loss of the water through
the urine, the burn wound, and insensible losses explain the per-
sistence of the pattern: lower volumes (with lower pressures)
decrease, while higher volumes accelerate, fluid excretion.
These forces tend to balance as the Brooke formula is
infused rapidly and then exhausted in all cases. The pattern is
dictated by the system structure that underlies the responses to
both the burn and the therapy, rather than specific values of the
20
parameters in the different cases.
Results of Case 9: Delayed Treatment
Case 9 displays the outcomes from a delay to 8 hours (four
additional bars) in the onset of treatment RXTM in a 40% burn. As
called for by the Brooke formula, the infusion rate is increased
so the prescribed volume RXW is administered within the first 48
hours postburn.
Dehydration deepens at the onset of therapy but the charac-
teristic response again recurs. By 36 hours, the patient des-
cends again into dehydration before maintenance water IVWM estab-
lishes a new equilibrium. Thus, doubling the delay in the onset
of treatment does not alter the fundamental response pattern.
Results of Case 10: Extreme Case Analysis
The previous cases have all varied from the base or modal
case by changing one factor or parameter at a time. Despite wide
variations, a consistent pattern of response occurs. Because of
the complexities of examining multiple combinations of nonmodal
parameter settings, we now examine a case where the parameters
are all selected to produce the most extreme possible response.
Consider a small (WIN=35 KG) patient with a large burn
(BSAB=.80), a large burn water loss multipler (BWLM=20), and a
delayed onset of treatment (RXTM = 8 hours). At burn time
(BRNTM=0), the burn water loss immediately leaps to almost 400 ML
per hour, then declines rapidly as the plasma water PW falls to
568
2.
1/3 its normal value at 4 hours, and to less than 10% of normal
at 8 hours.
Urine output UX virtually ceases at 2 hours and -- if the
patient were still alive -- the hematocrit HCT would have risen
to .87 by the time of treatment. All the parameters mentioned
respond rapidly to the Brooke formula infusion RXW2IV,
Unfortunately, the water loss from the burn wound itself
inereases to almost 500 ML per hour, as plasma water PW is forced
above its equilibrium levels, raising the vascular hydrostatic
pressure. This extraordinary water loss rate plunges the patient
into deepening dehydration again after 24 hours.
The water loss continues, with the administration on the
second day of an additional 3500 ML of fluid as called for by the
Brooke formula RXW. The dehydration is improved only slightly
with the renewal of maintenance water at 48 hours.
Despite the extreme values chosen for all the parameters,
and the fact that they are varied simultaneously, the response
exaggerates only slightly the fundamental pattern observed in
most of the previous cases, This demonstrates clearly that the
relationships among the factors, rather than their particular
values, determine the properties of the dynamic system response.
22
DISCUSSION (4.0)
The present, highly preliminary model is a radically dif-
ferent approach to the analysis of fluid therapy in acute burns,
which has been stalemated for over a decade. Detailed considera-
tion of the variables in fluid therapy casts enough light on
several obscure relationships, however, to believe that some sig-
nificant new understanding can be derived.
This may eventually include contributing to the formalized
methods of modeling biological (and other) systems, as the full
power of System Dynamics is brought to bear on medical scien-
tific, diagnostic, and therapeutic problems. The following dis-
cussion will suggest some directions that might produce such con-
tributions.
PRESENT MODEL STRUCTURE (4.1)
The plasma water volumes are valid (by definition) at known
equilibrium values, and the functions relating them to patients
of different sizes operate reasonably well over a broad range of
adult sizes, The method of simulating a burn injury, with its
control over the time, size, and water loss factors, gives suffi-
cient flexibility to compare it with data from a variety of clin-
ical and experimental situations.
Absolute burn area BSAB and the representation of the burn
water loss multiplier BLWM, or unit water loss per square meter,
is a well-defined area of uncertainty that was designed for sen-
23
sitivity analysis. Measurements of this factor have given
results varying between four and twenty times normal skin water
loss.
The model clearly demonstrates that burn water loss is
directly dependent on the unmeasurable state of hydration of the
patient, and that the unknown state of hydration confounds all
attempts at direct measurement. Futhermore, according to our
equations, the standard volumes of fluids called for by the
Brooke formula indicate that this factor cannot exceed sixteen
(BWLM < 16).
More precise evaluation, however, must await the insertion
of sodium and an interstitial space, Those relationships should
delimit the factor within a much narrower range.
Although -- given its present structure -- the general
responses of the model to different test functions are reason-
able, that structure itself is not realistic, producing the
unphysiologic features of the model's behavior.
The first deficiency of the present model is the realism of
the infusion rate, which is difficult to assess. The administra-
tion of intravenous fluids was inserted to give the model a real-
istic driver, even for preliminary examination. The declining
rate of administration (with a time constant of 16 hours)
represents the typically more rapid initial administration, while
fitting the Brooke prescribed quantities during each 8 and 24
hour interval.
569
24
In clinical practice, the fluid rate would be modified
according to the patient's response as demonstrated by urine out-
put, blood pressure, hematocrit, other signs and laboratory
values. The initial rate does seem too rapid, however, and the
decline to very low rates is too unresponsive to the actual clin-
ical situation, ‘The model requires a much smoother transition to
a new maintenance regimen, perhaps oral, to better emulate clini-
cal circumstances.
Accurate data on plasma volume are not available clinically
and the urinary output function is not precise enough for exact
feedback control of the IV infusion. Another use of the open
loop model, therefore, will be to let the large cumulative feed-
back experience embodied in the Brooke formulas serve as the
guide for a more sensitive and delicate control mechanism than is
possible without the aid of the preexisting formulae.
A second major deficiency of the present model is the
absence of an interstitial space, thet is, the space between the
capillaries and the cells that is approximately three times the
volume of the plasma itself. In the present model, water remains
in the vascular tree and pushes the blood volume, renal output,
burn, and other water losses to unrealistic heights.
The lack of an interstitial space, which serves as a reser-
voir that prevents the body from losing its fluid volume, exag-
gerates the response to the IV infusion. Our initial approaches
to adding an interstitial space reveal a conceptual phenomenon --
not necessarily a problem -- that we have not seen disscussed
25
expicitly in the classical or methodological literature on System
Dynamics [39-42].
Intravenous water equilibrates rapidly -- within 5 to 6
minutes -- with interstitial water, Given the hours-to-days
timescale of the overall analysis, we could represent the phy-
siologic functions governing the microcirculation (Starling's
laws) as instantaneous auxiliary relationships within each
integration interval.
The compliance functions for both the cardiovascular system
and the inserstitial space are highly nonlinear, however, so a
new equilibrium could not be determined without fitting and solv-
ing a set of complex equations. This is certainly contrary to
the spirit of System Dynamics, if it does not violate the law
overtly.
Such equations can be easily solved iteratively by assigning
them a short first-order time constant and still further shorten-
ing DT. It should be noted, however, that the dynamics of the
total problem do not require such a short integration interval;
it is required only by the mathematical solution of the nonlinear
equations.
While this may be convenient, we should be aware that we are
inserting levels and integrations where none are required to sub-
stitute for analytical solutions. This phenomenon may be more
widespread than has previously been realized, and, along with the
Euler integration algorithm, may contribute to some of the well-
570
26
known problems of "stiff" differential equations. We raise the
issue here for consideration and discussion.
Although not a defect of the model itself, clearly specified
relations between clinically observable symptoms and signs,
including mortality, would generate more specific touchstones
between the model, experimental data, and other observable, clin-
ical experience. More importantly, mortality would serve as a
value criterion (utility function or figure of merit) for choos-
ing among competing treatment’ alternatives.
Although the System Dynamics emphasis on stability criteria
was and still is critically important in identifying the system
and deciding on appropriate management to restore homeostasis,
almost all medical treatments induce a trajectory of disequili-
brium states before recovery. The price of these transient
states may be too high, given any reasonable concept of risk
aversion, for the final value gained in terms of longevity and
improved life quality, which would be limited to those who sur-
vive the treatment.
Thus, we cannot be satisfied to say simply that the curves
under different treatment regimens behave more or less similarly,
because even a 1 or 2% difference in mortality (on the average)
would be considered an important advantage for one of the treat-
ments,
27
PRESENT MODEL BEHAVIOR (4.2)
The present model seems to operate well with regard to
differences in body sizes. In further research the linear pro-
portionalities will be modified to account more precisely for
differences by age, sex, obesity, and other body builds.
The expression of many of the functions in ratios derived
from the standard person normalizes the model to "dimensionless"
quantities specific to the biological system at hand. This elim-
inates many spuriously specific measurements based on arbitrary
units, revealing the more fundamental structural causal relation
ships among the levels and rates.
Proper dimensionalization might enable a system of measure-
ment that would permit the statement of universal relationships
or biological "laws" across different sizes and shapes of partic
ular organisms, if not across species.
The plasma water and blood volume ratios PWR and BVR apply
the ratio concept to directly compare the responses of different
size patients to different stimuli. The ratios reflect only
differences in system structure and parameters, not irrelevant
differences in body size.
Even in its present elementary state, the model already
exhibits certain interesting complexities in its behavior. After
the initial burn, these are largely induced by the overlapping
control functions of turning maintenance water on or off, and the
quantity and rate of infusion of the IV fluid.
571
28
The patterns exhibited in the extreme case are incompatible
with life at several points. At present, however, the probabil-
ity of mortality is not included formally in the model. If it
had been, a pattern for mortality would almost certainly have
developed in the previous cases, and been exhibited here,
although in a more extreme form.
With sufficient treatment, however, all the patients in the
present model "survive", i.e., return to equilibrium, regardless
of the extremity of their condition at the onset of resuscita~
tion, Thus, without some end point criterion (such as mortality)
to serve as a reference, the results from different treatments
are difficult to evaluate. Such a function need not be exactly
correct to demonstrate the relative outcomes from different
treatment regimes.
RELATION OF MODELING TO DATA (4.3)
It is important to examine the validity issue using
appropriate concepts and terminology. Whether the model is
“yalid" or “invalid” is a poorly posed question that inhibits the
progressive empirical and conceptual synthesis, and integration
of new knowledge that is necessary to bring a model (and under~
standing) to a point where it gives new insight and begins to
suggest useful revisions of therapy and research.
Although the precedent is poor in all biology and social
sciences, progressive scientific understanding of a problem in a
basic and fundamental sense is nothing more than the progressive
29
revision of a model. In the early stages of model construction
(where we are now), implementing almost any informed suggestion
would improve the model and make it more valid and powerful than
it is currently.
Developing an appropriate approach to documentation of vali-
dity is a critical need for System Dynamics, It has been
estimated, for example, that investigations using System Dynamics
accelerated the development of an artificial pancreas for insulin
and glucose control by at least five years [43]. As we all know,
this involved trying dozens, or hundreds of presumably sensible
relationships that give unrealistic or even absurd behavior,
i.e., they are clearly and convincingly falsified in the routine
process of model construction. Yet these experiences rarely
appear in the model documentation (including ours).
Thus, the scientific reader asks the reasonable question
"How do you know the model is correct?," and cannot see the evi-
dence from the long sequence of tests that gradually constrainthe
model to conform to the real system. This is especially true for
the estimation of coefficients or structural relationships that
are still confused in current scientific research with "measure-
ment",
FURTHER RESEARCH AND MODEL DEVELOPMENT (4.4)
Substantial further development is necessary before this
preliminary model can be used to study realistic important ques-
tions. The most immediate extensions needed are the addition of
572
30
sodium, potassium and albumin to the plasma. All these com=
ponents (water, sodium, potassium and albumin) also need to be
modeled in the normal and burn interstitial and cellular spaces,
More realistic versions of the Brooke formula must be imple-
mented and other treatment regimens (colloid, hypertonic saline,
ete.) must be formulated. Further testing must be done for the
individual functional relationships, e.g., the renal control of
water.
Although not yet incorporated in the model, important prel-
iminary work has already been done on modeling capillary membrane
exchange and the action of the sodium-potassium "pump" operating
between the interstitial and cellular spaces. When these equa-
tions are operational, it will be possible to evaluate hypotheses
about varying capillary permeability and the probable effects of
different treatment formulas more confidently.
Beyond those relationships, the model should be extended to
hydrogen ion, one or more burn toxin factors, the effects of
other organs such as cardiac function, and the modification of
the size ratios for children and the elderly.
The most immediate result of a successful study would be
better guidelines for fluid therapy in general, and perhaps spe-
cial rules for clearly defined circumstances.
Once the model demonstrates a reasonable fit and follow of
previous and published data, then filters might be included to
estimate parameters for individual patients, as well as explore
31
the feasibility of incorporating the model directly into a feed-
back control loop.
The ultimate result could be refined on-line monitoring and
control of fluid, electrolyte and colloid infusion. This should
be tested extensively in animals before trials in patient treat-
ment.
573
32
CONCLUSION (5.0)
A preliminary model of plasma water loss and control has
been developed for acute burn patients, Given its structure, the
model gives reasonable responses to multiple external inputs,
including different body sizes, different sized burns, different
loss factors for water from the burn wound, and different levels
and times of treatment. With appropriate extensions, the model
offers a potentially powerful tool for investigating hypothesized
pathophysiological mechanisms for evaluating treatment alterna
tives and for adapting therapy to individual patients and supple-
menting their on-line control.
33
St. e
UY wk far.
Fig. 1
FLOW DIAGRAM FOR BURN RESUSCITATION MODEL
574
Fig 2(CASE 2):
‘SHORT
34
‘TER’ (30 HR) WATER DEPRIVATION
35
HRS
Fig. 2(CASE 3): 40% BURN, NO TREATMENT (KWi=0)
Fig 2(caSE 4): (BASE) 408 BUI HOT TREATMENT “(SROOKE)
575
36
Fig 2(CASE 5) ; Low BUR WATER LOSS FACTOR (BHII{ = 5)
. “TITLE? URN WATER Le
= FACTOR: EQUAL 3
TutEsS No A
BE BS SE Bo ao A
82
Qrecsess.
0...
0.
Fig 2(CASE 6): LARGE BURN WATER LOSS FACTOR (BWLM = 20)
37
—
= 8)
576
38
i
apes
'
‘
!
ee ee Se eee a
0..+++.+.-Total Water Givel
PibmfeW Nace ~
ATER,
Fig 2 (CASE 10): EXTREE CASE
LGRook'e *
Pen: roe tut A
Fe RATE:
=
°
>
Poa
39 577
B35: BURN FLUID RESUSCITATION MODEL 3, VERSION 5
----2-e PATIENT PARAMETERS - - - - - - -
WIN=70 KG WEIGHT NORMAL/NTL FOR PATIENT
WEIGHT RATIO [/]
WEIGHT [KG]
HEIGHT [IN]
WGHTR=WIN/WIN7O
WGHT. K=WTN-(PWQ-PW.K)/1000
HTIN=70
HTCM=2. 54*HTIN
BSA=.007184*EXP(.425*LOGN
APPENDIX 1
HEIGHT [CM]
(WIN) )#EXP(.725*LOGN(HTCM)) | BODY SURFACE AREA [M2]
BSAB=0,4 BODY SURFACE AREA BURNED [/]
BA=BSAB*BSA BURN AREA [M2]
> > > PLASMA WATER EQUATIONS =< < << < <
PW.K=PW.J+DT*(IVWM. JK+RXW2IV, JK-LWL. JK~
UX. JK-BWL. JK-SWL. JK) PLASMA WATER (ML)
PLASMA WATER
PWQ=BYN-RC PLASMA WATER
wee ee ee URINE OUTPUT EQUATIONS
URINARY EXCRETION [ML/HR]
URINE EXCRETION NRML [ML/HR]
URIN XCRTN NRML 70KG PT [ML/DY]
WGHT NRML 70KG PT [KG]
NTL/NRML [ML]
EQUILIBRIUM (ML)
PW=PWQ
UX. KL=UXN#UMBV. K*#PWR.K
UXN=WGHTR*UXN724/24
UXN724=1500
WINTO=70
UMBV. KsTABHL (UMBVT,BVR.K,0.4,1.4,.2)
URIN XCRTN MPR FM BLD VOL (ML/HR)
UMBVT=0.0/0.1/0.43/1.0/1.7/2.4
URN XCRTN MPR FM BLD VOL TABL
< << ¢ BLOOD VOLUME EQUATIONS < < < ¢
BLOOD VOLUME RATIO
BVR. {41
V.K/BYN
HCT. K=RC/BV.K HEMATOCRIT [/]
BLOOD VOLUME
RED CELL VOLUME [ML]
HEMOCRIT (NORMAL) (/)
BV.K=RC+PW.K (NL)
RCHCTN*BYN
HCTN=. 40
BYN=BVF *WTN*1000 BLOOD VOLUME NORMAL [ML]
*
a0
x >
40
BLD VOL FRCTN (OF ®GHT NRML) [/]
375
< << < SKIN WATER LOSS EQUATIONS < < < < ——
BWL.KLsBA*SWLFN*BWLM.K*PWR,K BURN WATER LOSS (KL/HR) py. 2
SWLFN=S11,14 ML/BR/M2 SKIN WATER LOSS FACTOR NRML
SWLTQ=BSA*SWLEN SKN WTR LSS TTL EQLBRM (ML/HR)
BWLM.K=1, 04+BURN.K BURN WATER LOSS MULTIPLIER (/)
BURN. K=STEP(BWLI, BRNTM) BURN WATER LOSS INCREMENT (/)
BRNTM=0 BURN TIME (TIME)
BWLI=9 BRN WIR LSS (MPR) INCRMNT (/)
PWR. K=PW.K/PHQ PLASMA WATER RATIO [/]
SWL. KL=SWLFN*USA*PWR.K (UNBURNED) SKN WTR LSS [ML/HR]
USA=BSA-BA UNBURNED SKIN AREA
INS, KL=SWL. JK+LWL. JK INSENSIBLE WATER LOSS
<< < < LUNG/GI WATER LOSS EQUATIONS < << <
LWL. KL=LWLQ*PWR.K LUNG/GI WATER LOSS [ML/HR]
LWLQ=WGHTR*LWL70D/24 LUNG/GI WTR LSS EQLBRM [ML/HR]
LWL70D=500 LUNG/GI WTR LSS 70KG PT (ML/DY)
o# #4 0 # # # TREATMENT EQUATIONS ### eo eH
IVWM. KL=I VWMQ*(1-STEP (MWCO, MWCOTM) +
MWCO*STEP(1,MWTOTM) ) MAINTENANCE WATER [ML/HR]
MWCO=1 MANTNC WTR CUTOFF(O=NOT CUT OFF;
1=MW OFF AT MWCOTM,CN AT MWTOTM)
MWCOTM=0 MW CUTOFF TIME (TIME)
MWTOTM=48 MW TURNON TIME [TIME]
TVWMQ=LWLQ+SWLTQ4U XN MNTC WATER ECBN (ML/HR)
RXW.K=RXW. J#DT*(RXFWI. JK-RXW2IV. JK)
RX WATER (IV) REMAINING [ML)
RXW=0 RX WATER NTL (BEFORE BURN) (ML)
RXFWI. KL =PULSE(FORMW/DT, RXTM, INTVL)
4@HR RX FORMULA WIR INPUT (ML)
FORMW=RXWCO*BROCKE 4eHR FORMULA FOR WATER (ML)
BROOKE=1.5*(2*WIN*BSAB* 100+
2000) BROCKE WTR 4@HR FCRMULA (ML)
°
az
41
RX IV WATER CUTOFF (OsCFr,? x
RXWCO=1 z
RXTM=4.0 HRS TREATMENT ONSET TIME SPPENDIX 1
x oO ae
INTVL=1000 LONG INTVL TO DEFER 2ND PULSES
TREATMENT WATER TO IV (ML/HR)
PRESCRIBED WATER CONTROL TIME
RXW2TV. KL@RXW.K/TVWRXT
IVWRXT = (48-RXTM) /3
IVWIT. Ke VWTT. J+DT*(IVWM. JK®STEP(1,0)+RXW21V. JK)
IV WATER TOTAL GIVEN [ML]
IWWTT=I WTTO IV WATER TOTAL INITIAL (ML]
IVWTTO=0
578
(17
2]
(3]
(5)
(6)
(7)
(8)
42
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