Dynamic Modeling of Peritoneal Dialysis and Its Implementation
in Children with Chronic Kidney Failure
0) 3 (4)
Gokalp E.° ’, Basar G6, Tekin D. » Barlas Y.
@ WBS Teaching Center, Warwick University, Coventry, UK
phd13eg@mail.whs.ac.uk
@) Dept. of Modeling, Simulation and Visualization Engineering, Old Dominion
University, 1300 Engineering & Computational Sciences Bldg Norfolk, VA, USA 23529
gbasa002@odu.edu
@ Turkish Airlines Inc. - Revenue Management Department, Demand Forecasting
Specialist
Contact: General Management Building Yesilkoy, Istanbul 34149 TURKEY
duygu.tekin@yahoo.com
a Industrial Engineering Dept. Bogazici University, 34342 Bebek, Istanbul,
TURKEY, ybarlas@boun.edu.tr
ABSTRACT
This study has been conducted to shed light on the dynamic interactions between the
peritoneal dialysis (PD) treatment and the nutritional intake decisions, with respect to the
physical development of children with chronic kidney failure. The interrelationships between
in, calcium, phosph sodium and potassium -the
major developmental and vital indicators of the child-patients - along with their relationships
the substances such as protein, alb
with the PD treatment have been analyzed with the help of System Dynamics methodology. To
analyze the dynamics of PD treatment, the time unit of the model has been chosen as a day
and the time horizon has been chosen as three years in order to better observe the differences
in the growth and devel of child-patients. Simulation experiments are carried out to
search for effective combinations of PD and nutritional recipes for child-patients. Finally, an
interactive simulation game version of the model, which represents the relationship between
the diet and the ratios of accumulated toxic or beneficial materials in the body, has been
designed. Such simulation game can be used to help doctors, patients and patients’ families
in seeking diet and tr recipes suitable to pati ’ monthly needs for a better growth
and physical development.
Keywords: Chronic Kidney Failure, Peritoneal Dialysis, Dialysis in Children, System
Dynamics, Simulation Modelling, Simulation Gaming
1. INTRODUCTION
Human body is a collection of numerous sub-systems that cooperate in order to keep
the internal balance, called “homeostasis”. Among those sub-systems, urinary system comes
to the forefront since it plays an important role to help maintaining vital indicators of the
body with its regulatory activities. Central components of the urinary system are kidneys.
When kidneys stop functioning properly, kidney failure occurs, toxic wastes
accumulate in the body, and the levels of materials found in blood such as albumin, calcium,
phosphate, active vitamin D, sodium and potassium go beyond their normal levels [1]. These
irregularities cause serious health problems such as high blood pressure, bone deformation
and protein-calorie malnutrition. In child-patients, growth retardation is one of the most
frequent symptoms of kidney failure [2].
1.1 Chronic kidney failure
Chronic kidney failure (CKF) is described as the decline in filtration function of
kidneys over time. Glomerular filtration rate (GFR) is used as the best measure to estimate
the level of kidney functioning, described as the volume of fluid filtered from the kidneys
over unit time. It can take values between 0 describing extreme failure to 100 describing full
health. This scale is used to determine the five stages of the disease. The last stage is called
“End Stage Renal Failure (ESRD)” in which GFR is under 15.
Organ transplantation and dialysis are two different treatments for ESRD. Former is a
surgery where damaged kidney is replaced by one from a healthy donor. Latter is divided into
two categories: peritoneal and haemodialysis. In child-patients, peritoneal dialysis is common
due to its flexibility with respect to children’s active social and school lives.
In ESRD patients, residual renal function (RRF) is important since it affects the
duration of dialysis, the life quality, and morbidity. RRF is described as the remaining
capacity of kidneys to remove wastes and toxic materials, or, remaining GFR capacity [3]. It
is observed that RRF declines linearly to zero over time independent of patients’ initial health
conditions.
1.2 Peritoneal dialysis
In peritoneal dialysis (PD), a soft tube, called “catheter”, is inserted into patient’s
abdomen to fill it with cleansing liquid, called “dialysis solution” or “dialysate”. Dialysate
remains in abdomen for a certain period of time until it drains toxic materials, extra fluids and
wastes from the body. After draining the toxic materials, it is exchanged with a clean
solution. This time period which dialysate remains in the abdomen is called “dwell time”.
Dialysate is composed of some electrolytes such as sodium, and magnesium and an
osmotic agent, glucose. The general diffusion principles are valid for PD and the difference in
concentration between blood and dialysate determines the amount of toxic materials
transmitted to dialysate. The transmission rate at which toxic wastes move to dialysate is
called “clearance rate.” Materials’ clearance rates are almost the same for different dialysates.
13 Complications
CKF patients suffer from several health problems. These problems can be categorized
as accumulation of toxic materials in blood, malfunctioning of protein metabolism, bone
deformation and imbalance of electrolytes.
First, CKF patients experience insufficient removal of toxic materials as a result of
protein metabolism such as urea and creatinine. Since protein is the main constituent of the
body, its anabolism and catabolism never stops, which means the formation of urea and
creatinine is inevitable in CKF patients. It is important to remove these toxic materials
through PD at regular intervals to provide normal protein metabolism functioning [1].
Albumin is the most abundant protein in blood. In CKF patients, decline in blood
albumin occurs due to improper protein metabolism. During dialysis, PD patients lose lots of
albumin. Even though the excessive loss of albumin triggers the production in the body, the
produced albumin is not enough to replace what is lost. Albumin level is used to detect and
track protein malfunctioning, and also it is a vital indicator for morbidity and mortality. In
order to keep and maintain the growth of child-patients at a healthy level, it is important to
prevent the decline in albumin level [4].
Calcium is a vital mineral for the growth and development of bones and crucial for
neural and hormonal systems in body. Another problem that CKF patients are facing is bone
deformation and retardation due to abnormal transition of calcium from bones to blood [5].
Also, diseased kidneys cannot excrete excessive phosphate, which causes build-up of
phosphate at fatal levels in the blood. To reduce its levels, patients use phosphate binders
through oral way [6].
Vitamin D also plays an important role in bone development. It is used in its active
form, called calcitriol, in the body. Calcitriol is produced in kidneys and helps reabsorbing
calcium from intestines. In CKF patients, calcitriol production stops. This causes excretion of
calcium directly from the intestines instead of its reabsorption. Consequently, patients with
CKF suffer from calcium deficiency. The need of calcitriol can be cured by oral medication
[1].
Another problem in CKF is the imbalance in sodium and potassium levels. Due to
improper kidney functioning, sodium cannot be excreted from the body sufficiently and
causes an increase in blood volume. This leads to high blood pressure. The removal of
potassium from the body also depends on kidneys’ functioning. Since CKF patients cannot
excrete potassium adequately, they suffer from high levels of blood potassium. Even a small
change in serum potassium levels can cause several fatal problems like heart attack.
Therefore, it is important to keep its level between normal values through dialysis [7] [8].
2. RESEARCH OBJECTIVES AND OVERVIEW OF THE MODEL
System dynamics (SD) approach is a method to describe, discuss and understand the
dynamics of complex systems and problems. Particularly, the complexity of medical
problems arises from the dynamic interactions between sub-systems in the human body.
Improper protein regulation and bone formation, along with disturbances in
electrolytes constitute the complexity and dynamics of the medical problem. Nonlinear
relationships between main factors in these sub-systems and the feedback loops that they are
connected with are the sources of the complexity of homeostasis. Adding the complexities of
PD to this system creates an even harder and more complicated problem.
The first objective of this study is to construct a model that describes the relationships
between PD, the related homeostatic activities in the body and the nutritional diets in
children. After building a valid model, the second objective is to carry out simulation
experiments to search the correct PD and nutritional recipes for child-patients. Final objective
is to develop an interactive game version of the model to help patients and their families
seeking better nutritional intake decisions.
In the study, the time unit is chosen as “a day” and simulation horizon is chosen as
“three years” to be able to observe adequately the effects of the disease and alternative
treatment methods on growth and development of child-patients.
2.1. Overview of the model
After a literature review, model is divided into three sectors: Bone Sector, Protein
Sector and Fluid-Electrolyte Sector (see Appendix 1) [10]. First two sectors are related to the
development and growth of children while the last one is important for vital indicators in the
body. In Figure 1, a general simplified representation of whole model can be found. In this
figure, stock variables in the model are shown in rectangle boxes. Stocks affecting all sectors
in the model are shaded rectangles, written in black. Stocks in the model are chosen as the
ones critical to control. These stocks are sodium (Na), potassium (K), calcium (Ca),
phosphate (PO), albumin, urea, creatinine, extracellular (blood) volume, muscle protein and
bone mineral content (BMC). Among these stocks, muscle protein and BMC are used as
physical indicators of growth in children. Flows in and out of stocks are determined by the
interactive relationships between hormones and nutrient intakes. Furthermore, the RRF, dwell
time, blood volume and the patient’s weight affect all sectors.
RRF level affects the loss of K, Na, water, PO, Ca, urea and creatinine through urine
positively. Since RRF declines linearly over time, the urine loss of mentioned materials also
declines linearly. In the model, based on the levels taken from real life patients, RRF starts
from 3 ml/min and declines to zero over the simulation horizon. Therefore, the urine loss of
mentioned materials also converges to zero. The second common factor is dwell time. Dwell
time increases the loss of albumin, urea, water, Na, K, Ca, PO and creatinine through PD over
time. Blood volume is used to calculate the concentration levels of albumin, Na, Ca, K, PO,
urea and creatinine in the blood. Last common parameter is patient’s weight. Since it is
assumed that the weight is proportional to the child-patient’s age, the amount of nutrition
intake in the body is determined based on body weight according to the medical guides
established for children with CKF. The loss of K, Na, Ca, creatinine, urea, PO, water and
albumin during PD depends on their concentrations in the blood. It means that when their
stock level increases, their PD losses also increase. Total decrease in the stock levels is
calculated as the sum of the amounts lost through urine and dialysis.
Finally, some of the protein is stored in the muscles for growth. If serum albumin
decreases under normal level, child-patients need extra protein to store. More protein intake
causes the formation of urea and creatinin. Therefore, there is a thin line between growth
maintenance and sufficient excretion of wastes.
Catab of albumin
PD loss of creat
U.lossof urea
Excretion K from,
gut,
+
U. loss of K
+
5 PO
iat
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PO binder
Cakeitriol level PO intake
Pd loss of KU. toss of
+
Pd loss of Na
% Joss of Na
y, U: lossof
“sf
_f* Geone
+
Bone absorb of Ca /
eMC
si
Na
Pdloss of Ca
+
Ca intake
Figure 1: The simplified version of model structure, variables, relationships
and parameters
3. MODEL DESCRIPTION
PD clearance rates of all elements in the model are determined through the clearance
Mass Transfer Coefficients (MTC) found in the literature. MTC has the unit of liter per time
showing the permeability of the element through the peritoneal membrane. Materials’ loss
rate through the PD are found by multiplying their MTC by their blood concentration and
then discarding it from the concentration of the material in dialysate [11]. Additionally,
except calcium and sodium, for all other elements in blood, the concentration in the dialysate
is equal to zero to maximize dialysis efficiency. In the model, PD clearance rates have the
unit of 1/day and daily dialysis duration for kidney patients are specified as 12
hours/ day, which is the usual case.
All the concentrations are found by dividing corresponding stock level by the blood
volume. The amount of loss by urine is affected positively by RRF and RRF’s decrease rate is
found as 0.17 ml/min/month in the literature [12]. All PD losses of the materials have linear
relationships with the PD time. The dialysate is assumed constant as “1.36% glucose” and PD
type is taken as Continuous Ambulatory Peritoneal Dialysis (CAPD) [4].
In the game version, body weight is taken as main input to calculate required food
intakes and stock levels. In simulation runs, the weight of the child starts from 10 kg and can
range between 10 and 50 (corresponding to the ages of 1 to 12) [13].
The blood test is done once a month and decision maker (DM) in the model changes
the nutritional intake and oral medicine levels according to its results. DM holds medicine
and nutritional prescription constant until the next month. To model the assumption that DM
would increase or decrease the nutritional intake levels when the concentration levels appear
to be high or low, proper functions are used affecting the nutritional intakes. Final nutritional
intake levels are found by multiplying these effect functions with required intake levels.
HISTORY(), MOD(Q) and TIME() functions are used to change the decisions just once in a
month in the model.
3.1. Bone sector
i, Background information
The indication of a normal growth in a child is the bone construction rate. This rate is
affected by the Ca balance between the blood and bone. As mentioned previously, the blood
Ca level in the children with CKF is lower than normal level. If there is not enough Ca in
blood, then Ca is released from the bones through blood, which diminishes the bones’
strength. The bone strength can be measured by BMC.
Ca blood level is affected by the parathyroid hormone (PTH), calcitonin and calcitriol.
When Ca blood level falls beyond normal, PTH increases and triggers the Ca transfer from
bones to blood. When Ca blood goes beyond normal, calcitonin hormone triggers the transfer
of Ca from blood to bones.
As mentioned earlier, Vitamin D affects the bone construction in children as well and
it is used in its active form, calcitriol. Since calcitriol triggers the reabsorption of Ca from
intestines, a decrease in its level due to CKF also causes a decrease in the blood Ca level.
4
ii. ions and si
Jf ip
One of the assumptions of this sector is about osteoblasts and osteoclasts which have
roles in the bone construction and destruction, continuously, non-stop during a day [1]. Since
the model time unit is a day, which makes the metabolic events of these cells too micro to
represent, they are not added to the model.
In the model, required calcitriol intake of the patient is satisfied with oral intake and
its production in the kidneys is taken as zero. Another assumption is that the phosphate
exchange between the bone and blood is negligible and it is not modelled.
6
iii. Bone sector model description
There are four stocks in this sector: Calcitriol, Blood Calcium, Blood Phosphate and
BMC (see Appendix 1-Figure 11). Blood Phosphate has two outflows as PD loss of PO and
urine loss of PO, and one inflow of absorption from the intestines. PD loss of PO is found by
multiplying phosphate clearance rate with the stock. Phosphate clearance is 0.33 for 12 hours
dialysis, 0.0275 per hour [14]. The other outflow is calculated by multiplying phosphate urine
loss rate with the stock. Phosphate urine loss rate is 0.09 /day for a RRF of Sml/min [14].
PO absorption from the intestines is affected by phosphate holder usage and calcitriol
level. As the calcitriol increases, the absorption increases. Normal calcitriol concentration is
57.9 ng/l. The absorption is found by multiplying phosphate intake with phosphate absorption
rate. The normal rate for absorption fraction is 0.65 but the phosphate holder usage decreases
this level. Absorption rate is found by multiplying the normal absorption rate with a graphical
function showing the effect of phosphate holder on phosphate absorption (see Appendix 2).
The blood phosphate level is effective at the phosphate holder intake which is modelled by
another effect function. The phosphate intake is found by multiplying normal phosphate
intake with the effect function of blood phosphate level (from the results of the blood tests) at
the phosphate intake (see Appendix 2). Therefore, if the blood phosphate level is higher than
normal, phosphate intake is decreased.
Another stock in the sector, calcitriol has one outflow and one inflow. Calcitriol
destruction rate is assumed to be | per day. The calcitriol intake to the body is a management
decision and thus affected by the blood Ca level. The required calcitriol intake increases as
the body weight increases [15]. Normal calcitriol intake for ESRD children is 10ng/kg/day
[13].
Blood Calcium is another stock in the sector. Like many other stocks in the model,
this stock has also a PD and a urine loss. But the Ca level in the dialysis fluid is really close to
blood level [16]. Ca clearance rate is 0.7 for a 12 hours dialysis. When RRF is 5ml/min, urine
loss fraction is 0.09 /day [17].
The absorption of Ca from the intestines depends on the calcitriol level [18]. As the
calcitriol level increases, the absorption increases, too. The absorption rate of Ca from the
intestines is taken as %11, while this level is %25 in healthy people [18]. Ca intake by the
food is a managerial decision and decided by checking blood test results and affects the
absorption. If the Ca level is higher than the normal level, then Ca intake is decreased for that
month. There is a required Ca level for a certain body weight.
Ca absorption is a bi-flow which is positive when Ca concentration is lower than
normal. This flow is formulated as classical stock adjustment formulation which has | as
stock adjustment time. The flow rate is affected by PTH when Ca level is lower than normal
and by calcitonin in the other case. These affects are shown by two effect formulations which
are multiplied by stock adjustment formulation to have the complete flow function (see
Appendix 2). On the other hand, PTH and calcitonin levels are affected by blood Ca level.
Normal blood PTH concentration at ESRD patients is at around 200 pg/ml which is higher
7
from healthy patients (<140 pg/ml) [15]. In blood, the normal level of calcitonin is around
200 pg/ml. This level is multiplied by the effect function of Ca to find the correct calcitonin
level [15].
3.2. Protein sector
iv. Background information
Body protein is another important indication of child growth and daily protein intake
should be enough to ensure a healthy growth. In children with CKF, protein intake is
restricted to prevent having dangerous urea and creatinine levels.
Albumin, the most abundant protein in blood, is generally used to observe nutritional
status of a child and it should be controlled frequently. In children with CKF, albumin level is
generally lower than expected because of its undesired loss from the blood during PD.
Urea and creatinine are dangerous waste products of metabolic activities and are
discarded via kidneys. In CKF patients, kidney function decreases by time and reaches to zero
which patients can no longer produce urine.
vw. A ions and simpli,
J iP
First, blood proteins other than albumin are not modelled since the changes in the
levels of other blood proteins are too small to be added in the model. The urine loss of
albumin is considerably small and thus it isn’t modelled [19].
Second, the inter-processes between muscle protein synthesis, protein intake, and
urea- creatinine formation are not included in the model. Muscle protein is assumed to be the
only protein stock in the model as it is the biggest source of protein store.
The child patient in the model is assumed to have an average physical activity in daily
life and it is assumed that the patient does not have metabolic acidosis condition.
vi. Protein sector model description
There are four stocks in the sector: albumin, urea, creatinine, and muscle protein (see
Appendix 1- Figure 12). The most important parameter is the protein intake. The required
protein intake is dependent on the body weight based on nutritional guidelines. If it appears
that the urea level is higher than normal according to blood test, the protein intake of the
patient is decreased. If the albumin level is lower than its expected level, then the protein
intake is increased. These effects of albumin and urea on the protein intake are modelled via
the several effect functions of which the details can be seen in the Appendix 2.
Albumin stock has two outflows of PD loss and albumin catabolism and has one
inflow of albumin synthesis. 0.73 g of the protein intake via foods is converted to albumin
every day [19]. On the other hand, albumin has a catabolism rate of 0.09 g/day [20]. The PD
loss of albumin is found by multiplying the albumin stock with PD clearance rate of 0.008 for
12 hours of dialysis which accounts for a day [19].
Urea in blood is lost by dialysis and urine and increased by the urea synthesis. PD loss
fraction is 0.07/ hour while urea loss fraction is 0.03/day/ml/min [21] [22]. Urea synthesis is
found by multiplying the protein intake with a constant synthesis fraction of 0.3/day (see
Appendix 2). Initial muscle protein level is linearly dependent on the body weight. For every
1 kg of body weight, there is 330 gram muscle protein for a normal child [23]. Muscle protein
has just one inflow which is found by multiplying the protein intake and synthesis fraction of
0.14/day with the effect function of protein intake on the muscle synthesis. As the protein
intake increases, the muscle protein synthesis increases as well.
The initial creatinine stock level is found by multiplying the blood volume with the
normal creatinine concentration of a child with 10 kg body weight. Creatinine synthesis
fraction is found as 0.027/day and urine loss fraction is found as 0.1/day for a S5ml/min of
kidney function while the PD loss fraction is found as 0.81/day for 12 hours of dialysis [24].
Creatinine concentration is normalized by dividing the real creatinine concentration with the
expected creatinine concentration for a given body weight.
3.3. Electrolyte sector
vii. Background information
Sodium affects the muscle and neural functions and the secretion of anti-diuretic
hormone (ADH) besides being main stimulant of thirst. Due to its effect in the blood volume
level, it indirectly affects the concentration of all other materials in the blood. As a result of
CKF, sodium cannot be removed from the body and accumulates in the blood.
The control of potassium in the body should be tight since it has important roles in
the water balance, muscle and neural functions like sodium [25]. For example, when
potassium level goes out of its normal boundaries, the heart rhythm deforms which can cause
heart attack. Potassium is excreted both via kidneys and intestines in a healthy body. Since
kidneys do not function properly in CKF patients, the excretion via intestines shows a 5 to
10% increase from its normal level [25]. Yet, this increase cannot satisfy the required
excretion rate of potassium. Thus dialysis has a crucial role in the prevention of the potassium
accumulation in blood.
viii. A ions and sii
The first simplification is that the loss of water via sweat is not modelled since this
loss does not affect any of the model parameters and its addition would not create any
dynamics. Also, there are many factors affecting the water intake in the body but only ADH
hormone is taken among these factors since the others aren’t related to the model scope. The
level of physical activity is not modelled either.
ix. Electrolyte sector model description
There are three stocks, potassium (K), sodium (Na) and blood volume in the sector
(see Appendix 1-Figure 13). Potassium has inflow of absorption from intestines, outflow of
gut losses, dialysis and urine losses, and cellular inflow. The loss from gut is found by
Can good jobs be profitable in low cost services?
A systemic model and estimation
Hazhir Rahmandad
hazhir@ mit.edu
Abstract
Can profit maximizing firms offer good jobs in low cost services? Assessing the viability of
good jobs in any setting requires the quantification of mechanisms connecting employee quality
and motivation, effectiveness of work processes, and customer service and integrating them at
the firm level to assess overall performance benefits and costs. In a dynamic model of service
operations we capture feedbacks, managerial decisions, costs, and benefits related to viability of
good jobs. Using data from Borders bookstores and utilizing extended Kalman filtering with
latent variables we estimate this model. We find evidence for significant benefits of employee
quality and building capabilities in this mainstream retail setting. Our results also suggest notable
managerial biases exist in allocating resources between customer service and capability building,
promoting the former as predicted by the capability trap hypothesis. We further find a sharp
discontinuity in the optimal organization of work within the range of parameters observed in this
setting, with a shift from low paying jobs to good jobs if cost of employee quality could be
contained below a threshold. The results point to potential viability of good jobs in low cost
services and offers a method for assessing these costs and benefits.
Keywords: Service, Retail, Good jobs, Capability Trap, System Dynamics, Kalman Filter,
multiplying constant loss rate of 0.25/day with the K stock level. PD loss fraction is
0.073/hour of dialysis. Urine loss fraction is 0.04/day per ml/min of RRF [26]. Absorption
from the intestines is equal to multiplication of K intake with the 0.75 absorption fraction.
The required K intake is calculated by using the body weight. The cellular flow of K is a bi-
flow which is formulated as a normal stock adjustment function. Normal K level is 0.17 g/l
and the stock adjustment time is taken as | day (see Appendix 2) [25].
Sodium has one inflow of absorption from the intestines and two outflows of PD and
urine losses. The absorption from the intestines is found by multiplying Na intake with the
absorption fraction of 0.6/day. The required Na intake is calculated by using the body weight.
Urine loss fraction is 0.003/day/RRF [27]. PD liquid has a really close Na concentration level
(3.05 g/l) to the normal blood Na concentration (3.15 g/l) which makes the PD loss of Na
residual [16]. The clearance rate of Na is 0.07 per hour of dialysis [28].
The initial level of blood volume stock is found by multiplying the initial body weight
with 0.2 I/kg [29]. Blood volume is lost via PD and urine and it is increased by the water
intake. Water intake level is found by multiplying the normal water intake with the effect
function of ADH in the water intake (see Appendix 2). Normal water intake is dependent on
the body weight. As the body weight increases, water requirement in the body also increases.
The PD loss fraction of blood volume is 0.26/day for 12 hours of dialysis [29]. Urine loss
fraction is 0.007/day per 1ml/min of RRF [30].
4. MODEL VALIDATION
4.1. Direct structure tests
In the direct structure tests, some direct tests are conducted such as unit consistency,
and direct extreme condition tests, without any simulations [31]. It is tested whether each
equation has unit consistency by entering the units of its input variables.
4.2. Indirect structure tests
Indirect structure (structure-oriented behavior) tests are done to compare the behavior
of the model with the (expected) real life behavior, in some extreme or other special condition
simulations. In the first test, all the stocks were held in their equilibrium levels [31]. The aim
behind this test is to assure that the system has a balanced structure which can yield
homeostasis, just like in the real life. In the second part of indirect structure tests, how the
system behaves under extreme conditions was tested. No dialysis, no protein intake, or
excessive protein intake can be counted as examples of extreme cases. Each of these extreme
cases is designed as simulation scenarios and the results are investigated to understand
whether the model gives reasonable results under these extreme scenarios [31].
The dynamics of the model in the case of no dialysis can be seen in Figure 2. The
blood volume and creatinine level reach a mortal state in a few days, which is consistent with
the real-life situation if no dialysis was made. These tests, demonstrate that the model
structure is consistent with the real system.
10
a
@ © EoF Volume z
8
s
fs
3
3
Figure 2: Extreme condition test: The dynamics of blood volume, creatinine
and urea when there is no dialysis
5. MODEL OUTPUT ANALYSIS
After the validation step, the base model has been run for 3 years starting with an
initial weight of 10 kg for a child patient. The dynamics of the base results for 1080 days can
be seen in Figures 3, 4 and 5 below. There are oscillations in the blood concentrations of most
variables since the nutrient intake decisions are changed just once in a month according to the
blood test results. Urea and normalized creatinine levels are a bit higher than their expected
levels during simulation, which is normal for an ESRD patient. As can be seen in the Table 1,
BMC and muscle protein levels at the end of the simulation are lower than those levels of a
non-patient child with same age. This can be interpreted as the indicator of a growth
deficiency in the child patient which is usually seen in children with ESRD.
2Na cone
ee
20 270.00 540.
8
810.00,
Figure 3: Base dynamics of electrolyte sector
11
Figure 5: Base dynamics of protein sector
Table 1 The comparison of muscle protein, BMC and blood volume of the base run with
a those levels of a non-patient child in the same age.
‘Time (aay) | “Body Mass(g)| “Muscle protein (p) Reso oo BMC Expected BMC
7 10 3300 3300 300 300
360 12 3884 3960 315 360
720 15 4501 4950 350 50
Final 18 ___ 5325590 |
6. SCENARIO ANALYSIS
In this section, the effects of initial RRF level, body mass, frequency of blood test, PD
duration, and protein and calcitriol intake on the growth level of the patient are investigated
through simulation runs.
12
6.1. The effect of initial RRF
In these runs, the effect of initial RRF level on the growth is tested. Angela et al.
found that patients with zero RRF generally have worse cardiovascular, inflammatory,
nutritional and metabolic profiles with a higher mortality rate [32].
Table 2 Initial RRF levels in different runs
Initial RRF Level
Run (ml/min)
1 0
2 10
3 20
st
As can be seen in Figure 6, blood volume is higher in 1 run in which RRF is lower,
which means higher blood pressure for such patients. This result is validated by the study of
Constantin et al. investigating the relationship between RRF and blood volume [33]. Since
urine loss of calcium, sodium and phosphate are negligible; they are not affected by RRF
level. As the RRF falls, the final muscle protein level is lower which indicates a slowed
growth. The reason behind a lower muscle protein level is the increasing urea concentration
and thus decreasing protein intake as RRF falls. This shows that growth is better maintained
in the uric patients (RRF is larger than zero) than the anuric patients (RRF is zero).
@ ECF Volume:
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Figure 6: Blood volume dynamics for different initial RRF levels
13
Paget
Figure 7: Muscle protein dynamics for different initial RRF levels
6.2. The effect of initial weight
In this analysis, the initial weight of the patient is determined as 10 kg and 30 kg
respectively in two different runs. Since the initial body weight level determines an initial age
in our model, the growth patterns in child-patient can be compared for different age levels.
Table 3 Initial body weight levels in runs
Run Initial body weight
1 10 kg
2 30 kg
The initial level of BMC is dependent on the initial body weight as explained in the
model description section. To be able to make a better comparison, BMC levels of two runs
are normalized by their expected BMC levels (without the illness) for the corresponding age
of the child. The same normalization process is done for muscle protein as well since it also
depends on the initial body weight. As it can be seen in Figure 8, in the second run, BMC
level is closer to its expected level than the i run. This shows that child patients who are
younger are expected to be more negatively affected by the illness in terms of their growth.
This finding is supported by the results found in literature as well [34].
14
@ norm BMC wth weight: 1-2 -
*:
t. wank |
ae %
p
20 270.00 ‘540.00 810.00 1080.0
= ne
Si 2 bore
Figure 8: Normalized BMC levels for two different initial body weights
7. GAME VERSION
After the construction, validation and verification of the model, an interactive
simulation game is designed to help parents and doctors of child patients in the treatment
process. The goal in the game is maintaining a normal growth level and keeping the
concentration levels within their limits. The game simulates two years and decisions are
entered in the interface once a month as shown in Figure 9. Before the game starts,
introductory information about the game is given along with a hand-out showing normal
blood concentration intervals of chemicals, required nutrient intakes and expected BMC and
muscle protein levels for different ages.
[uJ | _ Decision Set_~ |
Figure 9: The game decision interface
The game player is expected to enter nutrient and medicine intake level decisions, and
PD duration once a month while giving initial weight and RRF level only in the beginning of
the game. The concentration levels as a result of the decisions entered are shown once a
month to the player, while the muscle protein and BMC levels are shown just once every six
months. At the end of the game, a score is calculated based on how much the concentrations
have been outside their limits and how far the final growth parameters deviate from their
expected levels.
15
Figure 10: An example of game dynamics and final score
8. CONCLUSION
In this research, a dynamic model is built to understand the effects of peritoneal
dialysis and nutrient intake on growth and metabolic dynamics of child patients with chronic
kidney failure. After validating the model by direct and indirect structure tests, some
scenarios are tested to see the effects of important decisions like dialysis duration on the
growth of a child-patient. Additionally, an interactive game is designed to help the parents of
child-patients seeking a proper treatment of disease.
The model focusing on the growth of a child with chronic kidney failure comprises
three sectors: protein, bone and electrolyte. Modelling approach, assumptions and principles
for these sectors are explained in the model description section. Main input parameters are
initial body weight, initial residual renal function level and peritoneal dialysis duration. Even
though many simplifications are naturally done in modelling, validation and verification tests
have shown no obvious weakness in the structure or behavior of the model.
During the scenario analysis, the effects of peritoneal dialysis duration, initial level of
residual renal function and initial body weight on the growth patterns of children are
investigated. According to the results, doing peritoneal dialysis less than 12 hours decreases
the children’s growth rate while frequency of blood tests does not affect the results. Also, it is
found that if the child catches the illness at a younger age, the growth will be more negatively
affected.
In future studies, the model can be expanded by adding medical details such as the effects
of growth hormones and detailed nutritional components. Interactive game can also be improved
by changing the nutrient intake levels from grams to more common sense real life portions. Also,
the model can be enhanced to test other effects, such as alternative medication.
16
Acknowledgments
This research is supported by Bogazici University Research Grant no 8880.
9. REFERENCES
[1] A. C. Guyton and J. E. Hall, Textbook of Medical Physiology, Philadelphia: Elsevier
Inc., 2006.
[2] D. Hafner, “Effect of Growth Hormone Treatment on the Adult Height of Children with
Chronic Renal Failure,” The New England Journal of Medicine, pp. 923-930, 2000.
[3] L. M. Moist, F. Port, S. Orzol, E. Young, O. T., R. Wolfe, T. Hulbert-Shearon, C.
Jones and W. Bloembergen, “Predictors of Loss of Residual Renal Function among
New Dialysis Patients,” Journal of American Society of Nephrology, pp. 556-564,
2000.
[4] H. Gao, S. Lew and J. Bosch, “Biochemical Parameters, Nutritional Status and
Efficiency of Dialysis in CAPD and CCPD Patients,” American Journal of
Nephrology, vol. 19, no. 1, pp. 7-12, 1998.
[5] American Academy of Pediatrics-Committee on Nutrition, “Calcium Requirements of
Infants, Children, and Adolescents,” Pediatrics, pp. 1152-1157, 1999.
[6] K. Kalantar-Zadeh, “Clinical Outcomes of Hypocalcemia in Chronic Kidney
Disease,” US Nephrology, pp. 19-23, 2008.
[7] M. Lilova, “Hypertension in Children with Chronic Renal Failure,” The Turkish
Journal of pediatrics, pp. 28-31, 2005.
[8] A. Werynski, J. Waniewski and B. Lindholm, “Kinetic Modeling of Fluid and Solute
Transport in Peritoneal Dialysis,” Frontiers of Medical and Biological Engineering,
pp. 105-115, 2000.
[9] J. Homer and G. Hirsch, “System Dynamics Modeling for Public Health: Background
and Opportunities,” American Journal of Public Health, pp. 452-458, 2000.
[10] E. Gokalp, G. Basar, D. Tekin and Y. Barlas, “Dynamic Modelling of Peritoneal
Dialysis and Its Implementations in Children with Chronic Renal Failure,” Bogazici
University, Istanbul, 2012.
[11] F. A. Gotch, “Kinetic Modeling of Continuous Flow Peritoneal Dialysis,” Seminars in
Dialysis, vol. 14, no. 5, pp. 378-383, 2002.
[12] R. Lopez-Menchero, “Importance of Residual Renal Function in Continuous
Ambulatory Peritoneal Dialysis: Its Influence on Different Parameters of Renal
Replacement Treatment,” Nephron, vol. 83, no. 3, pp. 219-225, 1999.
[13] National Kidney Foundation, “KDOQI Clinical Practice Guideline for Nutrition in
Children with CKD,” American Journal of Kidney Disease, vol. 53, no. 3, p. Supply
2,2009.
[14] R. Goldman and S. H. Bassett, “Phosphorus Excretion in Renal Failure,” The Journal
of Clinical Investigation, vol. 33, no. 12, pp. 1623-1628, 1954.
17
[15] O. Simonsen, D. Venturoli, A. Wieslander, O. Carlsson and B. Rippe, “Mass Transfer
of Calcium across the Peritoneum at Three Different Peritoneal Dialysis Fluid Ca2 and
Glucose Concentrations,” Kidney International, vol. 64, pp. 208-215, 2003.
[16] C. H. Hsu, “Are We Have Mismanaging Calcium and Phosphate Metabolism in Renal
Failure?,” American Journal of Kidney Diseases, vol. 29, no. 4, pp. 641-649, 1997.
[17] C. P. Schmitt, G. Ardissino, S. Testa, A. Claris-Appiani and O. Mehls, “Growth in
children with chronic renal failure on intermittent versus daily calcitriol,”
Pediatric Nephrology, vol. 18, no. 5, pp. 440-444, 2003.
[18] I. Hornum, “The disturbance of calcium metabolism in chronic renal failure,” in
ERA- EDTA Proceedings, 2011.
[19] G. A. Kaysen, V. Rathore, G. Shearer and T. A. Depner, “Mechanisms of
hypoalbuminemia in hemodialysis patients,” Kidney International, vol. 48, no. 2,
Pp.
510-516, 1995.
[20] G. Kaysen, J. Dubin, H. Miiller, W. Mitch, L. Rosales and N. Levin, “Relationships
among inflammation nutrition and physiologic mechanisms establishing albumin
levels in hemodialysis patients,” Kidney International, vol. 61, no. 6, pp. 2240-2249,
2002.
[21]R. Krediet, C. Douma, R. van Olden, M. Ho-dac-Pannekeet and D. Struijk,
“Augmenting solute clearance in peritoneal dialysis,” Kidney International, vol. 54, no.
6, pp. 2218-
2225, 1998.
[22] G. Montini, G. Amici, S. Milan, M. Mussap, M. Naturale, I. Ratsch, A. Ammenti, P.
Sorino, E. Verrina, B. Andreetta, G. Zacchello and I. R. o. P. P. Dialysis., “Middle
molecule and small protein removal in children on peritoneal dialysis,” Kidney
International, vol. 61, no. 3, pp. 1153-1159, 2002.
[23] C. E. Webber and R. D. Barr, “Age and Gender Dependent Values of Skeletal
Muscle Mass in Healthy Children and Adolescents,” Journal of Cachexia Sarcopenia
Muscle, vol. 3, no. 1, pp. 25-29, 2011.
[24] J. T. Brosnan, R. P. Da Silva and M. E. Brosnan, “The Metabolic Burden of Creatinine
Synthesis,” Amino Acids, vol. 40, no. 5, pp. 1325-1331, 2011.
[25] J. Ahmed and L. S. Weisberg, “Hyperkalemia in Peritoneal Dialysis,” Seminars
in Dialysis, vol. 14, no. 5, pp. 348-356, 2002.
[26] J. F. Gennari and A. S. Segal, “Hyperkalemia: And Adaptive Response in Chronic Renal
Insufficiency,” Kidney international, vol. 62, no. 1, pp. 1-9, 2002.
[27] S. Davies, O. Carlsson, O. Simonsen, A. Johansson, D. Venturoli, I. Ledebo, A.
Wieslander, C. Chan and B. Rippe, “The effects of low-sodium peritoneal dialysis
18
fluids on blood pressure, thirst and volume status,” Nephrology Dialysis
Transplantation, vol.24, no. 5, pp. 1609-1617, 2009.
[28] O. Ortega, P. Gallar, A. Carrefio, M. Gutierrez, I. Rodriguez, A. Oliet, A. Vigil and E.
Gimenez, “Peritoneal sodium mass removal in continuous ambulatory peritoneal
dialysis and automated peritoneal dialysis: influence on blood pressure control,”
American Journal of Nephrology, vol. 21, no. 3, pp. 189-193, 2001.
[29] W. Smit, M. Langedijk, N. Schouten, N. van den Berg, D. Struijk and R. Krediet, “A
comparison between 1.36% and 3.86% glucose dialysis solution for the assessment
of peritoneal membrane function,” Peritoneal Dialysis International , vol. 20, no. 6,
pp.734-741, 2000.
[30] B. R. Don and G. Kaysen, “Serum Albumin Concentration and Chronic
Kidney Disease,” US Nephrology, vol. 5, no. 1, pp. 20-27, 2010.
[31] Y. Barlas, “Formal aspects of model validity and validation in system dynamics,”
System Dynamics Review, vol. 12, no. 3, pp. 183-210, 1996.
[32] A. Y. Wang, J. Woo, M. Wang, M. M. Sea, J. E. Sanderson, S. F. Lui and P. K. Li,
“Important differentiation of factors that predict outcome in peritoneal dialysis patients
with different degrees of residual renal function,’ Nephrology Dialysis
Transplantation, vol. 20, no. 2, pp. 396-403, 2005.
[33] C. J. Konings, J. P. Kooman, M. Schonck, D. G. Struijk, U. Gladziwa, S. J. Hoorntje, A.
W. van der Wall Bake, F. M. van der Sande and K. M. Leunissen, “Fluid status in
CAPD patients is related to peritoneal transport and residual renal function: evidence
from a longitudinal study,” Nephrology Dialysis Transplantation, vol. 18, no. 4, pp.
797-803, 2003.
[34] A. Quan and M. Baum, “Protein Losses in Children on Continuous Cycler Peritoneal
Dialysis,” Pediatric Nephrology, vol. 10, no. 6, pp. 728-731, 1996.
19
APPENDIX 1: STELLA VIEW OF THE MODEL
we. 4
oR absart fr a
effect PO bing on AO
£0 Gaon | Nom abso ir PO
;
fect Ca on cabot in
“Ny
effeot Calcitonin on bore absorb Norm PTH fevel
Figure 11 Bone sector stock-flow diagram
20
Creat poo! in body Musole prt
A
ee ihn
Figure 12 Protein sector
21
stock-flow diagram
Figure 13 Electrolyte sector stock-flow diagram
22
