THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 293
DYNAMIC ANALYSIS OF THE INFLUENCE OF REANIMATION TREATMENT
IN BURNED PATIENTS.
Gomez-Cia, T. (*)
Roa Romero, Laura (&)
Lazo Zbykowski (*)
(*) Hospital "Virgen del Rocio", Sevilla.
(&) E.T.S. Ing. Industriales,’ Sevilla.
ABSTRACT
A non-lineal mathematical model of capillary dynamic has been
constructed to study the reanimation stage and the effect that
different treatments have on burn patients.
This analysis allows a qualitative and quantitative knowleage
of the dynamic behaviour of variables very difficult to
quantify in daily practice, like plasma volume, net liquid
shift in burned and non-burned areas, etc.
The value and fidelity of the model was obtained by comparison
of the reckoned results with those measured in a serie of
patients of the Burn Unit of a General Hospital.
INTRODUCTION
It is known that burn injury causes an alteration that consids
in an increment of protein and liquid shifts from plasma to
interstitial compartment. If the shifts are important, charac-
teristic in burns of considerable extension, a shock by
decrease of plasma volume appears, Artuson (1979a, 1984b).
The protein shifts, related to burn surface area (BSA), de-
crease the plasma oncotic pressure, and oedema develops in
non-burned areas by increment of liquid shifts. Commonly, the
protein shifts have been related with the molecular weight,
in the way that those of less diameter would have more facility
to extravasation (Carvajal 1979a, 1980b).
The greatest change occurs in the three first hours after
injury and return with time to initial values.
We present a mathematical model of capillary permeability to
make a dynamic analysis of initial reanimation and of the
influence that protein and liquid administration have in burn
patients, with special emphasis in dynamic behaviour of the
variable plasma oncotic pressure. The results obtained by
simulation are compared with those measured in a series of
burn patients.
294 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
MATERIAL & METHODS
Construction of the model.
The methodology followed in model construction has been the
dynamic system approach, Forrester (1968), and three consecu-
tive stages have been developed:
1) Construction of a model of capillary dynamic in normal
conditions for a mean person.
The extracellular space considered has been divided in two
compartments, plasma and interstitium. The simplified causal
diagram, where the relations between the variables that take
place in liquid exchange at capillary level are defined, is
shown in Figure 1. The equations of state variables, which
define the mathematical model, are based on the assumptions
considered in the majority of macroscopic hemodinamic studies,
Leonard (1973), Abbrecht (1980) and Roa (1982):
aPV/dt = Qf - Que - Qs + Qreab +#Qlimph qq)
dIV/dt = Qs - Qreab - Qee - Qlimph (2)
aPP/dt = Jf - Js + Jlimph (3)
aIP/dt = Js - Jlimph (4)
Where PV = plasma volume, IV = interstitial volume, PP =plasma
proteins, IP = interstitial proteins, Q = liquid flows, J =
protein-flows, (f = intravenous fusion, ue = urine eliminated,
s = shifts, reab = reabsortion, limph = flow by limph, ee=
eliminated by evaporation).
The different behaviours of the model are obtained acting over
the control variables: intravenous fusion of liquids and
proteins and diuresis.
The validity of the model has been contrasted by comparison
of the obtained results with the measured by different authors
Guyton (1971).
The sensitivity of the model has been analysed by the sucessie
passages and the Montecarlo methods, verifying how the beha-
viour depends on the structure of the model, independently of
the values of the initial conditions and parameters; meanwhile
these remain in phisyological limits.
2) Burn injury adaptation for different person.
From weight and height values of the patient, the initial
conditions are obtained in Topley and Jackson Tables (1962).
In this stage two zones are planed in the model: burned and
non-burned areas. The burn surface area (BSA), obtained in
Lund and Browder (1944) Charts, is added to control variables.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 295.
3) Simulation of treatments.
Knowing the alterations of burn injury, a factor to be taken
into account in the initial stage of treatment is the quantity
and quality of protein administration, In this way, to calcu-
late the plasma oncotic pressure in function of every plasma
protein fraction we propose the following equations:
POPE = a + b * PPTE + c * PPTf2 + d * ppre3 (5)
iss
POPp = ¥ POPE
isl
Where POPf = plasma oncotic pressure of a protein fraction,
PPT£ = plasma protein fraction in plasma, POP, =plasma oncotic
pressure; a,b,c and d are the adequated coefficients for every
fraction (Table I).
Clinical Study
A series of patients has been studied with burns comprised
between 15 and 95 % of BSA. As part of the usual diagnostic
and control procedures in this type of patients were determimi
frequently, during the first hours after the burn injury, the
hematocrit value, plasma protein concentration, intravenous
fusion of liquids and proteins and diuresis, among other para-
meters. Moreover, the evolution of the weight of the patients
was registered continously by means of a bed scale.
RESULTS
In constrast of the validity and utility of the mathematical
model we present the results obtained in a patient, that were
verified in the ramainder cases.
In Figure 2 the variations, during the 15 hours after burn,
of the values of hematocrit, as measured and as obtained by
simulation, are represented, showing that the behaviour of
this variable, that defines the proportion between red blood
cells and plasma, is characterized by an increment, expression
of liquid shifts after burn injury.
In Figure 3, the behaviour of variable plasma protein concen-
tration, as measured and as simulated, shows a decrease, mean-
while the hemoconcentration, indicative of protein shifts from
plasma to interstitium.
In Figure 4 the evolution of variables increment of patient's
weight ‘and variation of calculated extra cellular volume are
represented. The evolution is consistent with the oedema that
this patient experimented.
The dynamic behaviour of variables like plasma volume, plasma
oncotic pressure, liguid shifts from plasma to interstitial
compartment in burned and non-injuried area, all of them very
difficult to quantify in daily practice, are represented in
296 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
Figure 5.
CONCLUSIONS
The mathematical model, that we present, provides a vision
from a macroscopic and global point of view of the dynamic
capillary alterations in burned patients. It permits a qualita
tive and quantitative knowledge of thé dinamic behaviour of
variables very difficult to quantify in.daily practice that
are very indicatives of the real situation of the rehydrata-
tion of the patient.
It emphasises the dynamic behaviour of the system in front
of the different intravenous fusion of liquids and proteins,
that can be of significant importance in the reanimation
treatment of these patients.
The results obtained agree with the consulted references and
integrate in an homogenous block the conclusions of different
authors on this subject.
The described mathematical model permits to study a priori
what will be the behaviour of the real system, the patient,
in front of a treatment and what would be the result if it
were modified.
One advantage which must be emphasized is its accessibility
to people not expert in computer sciences.
ACKNOWLEDGEMENTS
This work has been supported in part by the C.A.I.C.¥.T.
REFERENCES
_ Abbrecht, P.H. (1980) Regulation of extracellular fluid volume
and osmolality. Ann. Biomed. Engineer. 8:461-480.
Arturson, G. and Lousson, C.E. (1979a). Transcapillary trans-
port after thermal injury. Scand. J.Plast. Reconstr.
Surg., 13: 29-36.
Arturson, G., Groth, A., Hedlund, A. and Zaar, B. (1984b).
Potential use of computer simulation in treatment of
burns with special regard to oedema formation. Scand.
J. Plast. Reconstr. Surg., 18: 39-47
Carvajal, H.F., Linares, H.A. and Brouhard, B.H. (1979a).
Relationship of burn size to vascular permeability
changes in rats. Surg. Gynecol. Obstet. 149: 193-198.
Carvajal, H.F. and Linares, H.A. (1980b). Effect of burn depth
upon oedema formation and albumin extravasation in
rats. Burns, 7: 79-83.
Forrester, J.W. (1968). Principles of systems, Wringht-Allen
Press.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 297
Guyton, A.C,., Granger, H.J. and Coleman, T.F. (1971). Auto-
regulation of the total sytemic circulation and its
relation to control of cardiac output and arterial
pressure. Circul. Res., 29/1: 93-97.
Leonard, J.I. and Abbrecht, P.H. (1973). Dinamics of plasma~
interstitial fluid distribution following intravenous
fusion in dogs. Experimental and Computer simulation
study. Circul. Res., 33: 735-748.
Lund, C. and Browder, N. (1944). The estimation of areas of
burns. Surg. Gynecol.& Obst., 79: 352-359.
Topley, E., Jackson, D., Mac, G. and Cason, J.S. (1962).
Assesment of red cell lossin the first two days after
burns. Ann. Surg., 155: 581-586.
Fig.
INTERSTITIAL PLASMA
VOLUME a ae VOLUME
+ INTERSTITIAL NET LIQUID + HYDROSTATIC ia
HYDROSTATIC -————— FLOW AT THE 4 “S*~————__ PRESSURE AT
PRESSURE CAPILLARY LEVEL CAPILLARY LEVEL
ss + =
INTERSTITIAL PLASMA
COLOIDOSMOTIC ONCOTIC
PRESSURE PRESSURE
1: Simplified causal diagram of liquid exchange at the capillary level.
9861 ‘Y3GO.LDO ‘WTTIARS “AL3IOOS SOINVNIG WALSAS 3H 40 3ONSY34INOD TWNOILVNUSINI 9861 3HL 862
TABLE I: Coeficients of equation (5) to calculate
fraction (Pf)
Pt a b
x, 1166378 2.538474
a“ 2 -8.407558E-03 1.20017
9.488872E-03 +6527875
rad 4,.562615E-02 + 1889091
Alb. -2.924623E-02 2.271142
the plasma oncotic pressure of a protein
1.124984
9.419518E-02
+1246588
«1967993
1336642
-3.018779E-02
8.718739E-03
~1.485755E-03
-6.295053E-03
1.512775E-02
66% 9861 ‘H3GOL90 ‘VTTIASS ‘ALZIDOS SOINVNIG WALSAS 3HL JO JONIYIANOD TWNOILVNYSLNI 9861 SHL
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SULIETY. SEVILLA, ULTUBER, 1900
HEMATOCRIT VALUE
O° HC NER
MULATED
Fig. 2: Dynamic behaviour of variable hematocrit value.
PLASMA PROTEIN CONCEN.
cS
=
&
=
iS
=
2
o
=
sl
a
1a
TIME CHCURS >
O PPC MEASURED + PRC SIMULATED
Dynamic behaviour of variable plasma protein concentra
tion.
Fig.
WEIGHT VARIATION
BEEK,
2860
16616}
WEIGHT VARIATION <BR)
-ieeek
8
TIME 2
OW. MEASURED = ° SIMULATED
Fig. Dynamic behaviour of weight variation.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
Fig.
POP < MMHG?
TI COCeMIND
Ss
PLASMA VOLUME
a
oe
18)
al
Oo Tl HOH-BURNED
* TI BURHED AREA
zal : :
Variables obtained by simulation.
301
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