i UNIVERSITI MALAYSIA PAHANG DECLARATION OF THESIS AND COPYRIGHT Author’s full name : SIVA A/L GOPALAKRISHNAN______________________ Date of Birth : 3 MARCH 1992_______________________________ Title : INVESTIGATION ON DIFFERENT TYPES OF BLOOD GLUCOSE CONTROL SYSTEM. Academic Session : 2015/2016___________________________________________ I declare that this thesis is classified as: CONFIDENTIAL (Contains confidential information under the Official Secret Act 1972)* RESTRICTED (Contains restricted information as specified by the organization where research was done)* OPEN ACCESS I agree that my thesis to be published as online open access (Full text) I acknowledge that Universiti Malaysia Pahang reserve the right as follows: 1. The Thesis is the Property of Universiti Malaysia Pahang. 2. The Library of Universiti Malaysia Pahang has the right to make copies for the purpose of research only. 3. The Library has the right to make copies of the thesis for academic exchange. Certified By: ________________________________ ____________________________ SIVA A/L GOPALAKRISHNAN Dr. UMMU KULTHUM bt JAMALUDIN 920307-03-5411 Date: Date:
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i
UNIVERSITI MALAYSIA PAHANG
DECLARATION OF THESIS AND COPYRIGHT
Author’s full name : SIVA A/L GOPALAKRISHNAN______________________
Date of Birth : 3 MARCH 1992_______________________________
Title : INVESTIGATION ON DIFFERENT TYPES OF BLOOD
GLUCOSE CONTROL SYSTEM.
Academic Session : 2015/2016___________________________________________
I declare that this thesis is classified as:
CONFIDENTIAL (Contains confidential information under the Official
Secret Act 1972)*
RESTRICTED (Contains restricted information as specified by the
organization where research was done)*
OPEN ACCESS I agree that my thesis to be published as online open
access (Full text)
I acknowledge that Universiti Malaysia Pahang reserve the right as follows:
1. The Thesis is the Property of Universiti Malaysia Pahang.
2. The Library of Universiti Malaysia Pahang has the right to make copies for the
purpose of research only.
3. The Library has the right to make copies of the thesis for academic exchange.
Certified By:
________________________________ ____________________________
SIVA A/L GOPALAKRISHNAN Dr. UMMU KULTHUM bt JAMALUDIN
920307-03-5411
Date: Date:
ii
UNIVERSITI MALAYSIA PAHANG
FACULTY OF MECHANICAL ENGINEERING
I certify that the project entitled “Investigation on different types blood glucose
system” is written by Siva Gopalakrishnan. I have examined the final copy of this
project and in our opinion; it is fully adequate in terms of scope and quality for the
award of the degree of Bachelor of Engineering. I herewith recommend that it be
accepted in partial fulfillment of the requirements for the degree of Bachelor of
Mechanical Engineering.
Examiner: Signature:
3
SUPERVISOR’S DECLARATION
I hereby declare that I have checked this project and in my opinion, this project is adequate in
terms of scope and quality for the award of the degree of Bachelor of Mechanical Engineering.
Signature :
Name of Supervisor : Dr Ummu Kulthum bt Jamaluddin
Date :
4
STUDENT’S DECLARATION
I hereby declare that the work in this thesis is my own except for quotations and summaries
which have been duly acknowledged. The thesis has not been accepted for any degree and is not
concurrently submitted for award of other degree.
Signature :
Name : SIVA GOPALAKRISHNAN
ID Number : MG12029
5
INVESTIGATION ON DIFFERENT TYPES OF BLOOD GLUCOSE CONTROL
SYSTEM
SIVA A/L GOPALAKRISHNAN
Thesis submitted in fulfilment of the requirements for the award of the degree of
Doctor of Philosophy/Master of Science/Master of Engineering
Faculty of Mechanical Engineering
UNIVERSITI MALAYSIA PAHANG
JUNE 2016
6
Dedicated to my parents
7
ACKNOWLEGMENT
It is such a pleasure and I would like to take this golden opportunity to thank my Supervisor, Dr.
Ummu Kulthum bt, Jamaludin for her germinal ideas, invaluable guidance, continuous
encouragement and constant support in making this research possible. I am very grateful and
appreciate her support and help, without her, I couldn’t manage to finish my final year project on
time I am truly grateful for her progressive vision about my training in science, her tolerance of
my unexpected wrong doings, and her commitment to my future career. I also sincerely thanks
for the time spent proofreading and correcting my many mistakes. Throughout this project, I
learn to be more independent and gain some knowledge in handling software.
I would like to thank my parents for their support whenever I feels down and gives me
encouragement so that I won’t give up so easily. I’m also grateful to my elder sister for giving
me tips and idea regarding the project. It is essential to finish this final year project in order to
complete my degree in Mechanical Engineering field.
8
ABSTRACT
This thesis focus on investigation on different types of blood glucose control system. Basically it
is a case study on proposed blood glucose protocols. Among the protocols been implemented in
Intensive Care Unit or critically ill patients were been studied and the outcome of this project is
to propose the suitable blood glucose protocol for critically ill patients in Malaysia. This thesis
refers back a collection of journals regarding the different types of blood glucose protocols
together with the algorithm mathematical model as a general view. Two main protocols known
as HTAA and SPRINT been implement in Hospital Tengku Ampuan Afzan,Malaysia and
Christchurch Hospital, New Zealand respectively. Besides of studying whether both protocols
are capable to reduce the mortality rate, these two are compared in terms of patients suitability
whether they can adapt to the current protocols or not. Next, is to find out whether both protocols
are same in their goal and the significant level of the patient’s data obtained from both hospitals
(HTAA and Christchurch). In order to find out the patients data is significant or not and the goal
of the protocols whether similar, some statistical analysis been carried out solidify the hypothesis
statement. This is to ensure the outcome statement of proposing the best protocol between
HTAA and SPRINT to critically ill patients in Malaysia.
9
ABSTRAK
Tesis ini berfokus kepada kaji selidik atas pelbagai jenis sistem kawalan glukos darah. Secara
umum, projek ini merupakan kajian kes berdasarkan protokol glukos darah yang telah
dicadangkan. Berdasar kepada protokal yang digunakan di Unit Rawatan Rapi atau pesakit
kritikal telah dikaji dan kesimpulan daripada projek ini ialah mencadangkan protokal yang paling
sesuaik kepada para pesakit kritikal di Malaysia. Kajian kes telah di buat melalui koleksi
pembacaan artikel dan jurnal berkenaan jenis protocol dan algoritma model matematik yang
berkaitan antara satu sama lain secara umum. Dua protokol yang di kenali sebagai HTAA dan
SPRINT masing-masing digunakan di Hospital Tengku Ampuan Azfzan dan Hospital
Christchurch, New Zealand. Selain mengkaji sama ada kedu-dua protokol dapat mengurangkan
kadar kematian dalam kalangan pesakit kritikal, tidak terlepas perbandingan antara kedua-dua
protokol ini dari segi kesesuaian pesakit kritikal dalam mengadaptasi protokol-protokol tersebut.
Di samping itu, kaji selidik ini bertujuan untuk mengenalpasti sama ada kedua-dua protokol
menpunyai fungsi yang sama atau sebaliknya serta mengetahui keketaraan data pesakit-pesakit
daripada duah buah hospital (HTAA dan Christchurch). Oleh itu, sesetengah analisis statistik
telah dibuat bagi mengkukuh penyataan hipotesis yang membuktikan pemilihan protokol yang
sesuai kepada para pesakit kritikal di Malaysia.
10
TABLES OF CONTENTS
LIST OF FIGURES 13
LIST OF TABLES 14
CHAPTER 1 17
INTRODUCTION 17
1.1 Introduction 17
1.2 Problem Statement 18
1.3 Objectives 18
1.4 Project Scope 19
CHAPTER 2 20
LITERATURE REVIEW 20
2.1 Introduction 20
2.2 Type of Diabetic Patient 21
2.2.1 Type-1 Diabetic Patient 21
2.2.2 Type-2 Diabetic Patient 21
2.3 Introduction of Hyperglycemia and Hypoglycemia 22
2.3.1 Hyperglycemia 22
2.3.2 Hypoglycemia 23
2.4 Introduction of Artificial Pancreas 23
2.4.1 Close Loop System for an Artificial Pancreas 25
2.5 Introduction of Algorithm 25
2.6 Algorithms 26
2.6.1 Model Based Predictive Control 26
2.6.2 Input-Output Controller Model 27
2.6.3 Linear Model Predictive Control (Linear MPC) 34
2.6.4 Model Predictive Control with State Estimation (MPC/SE) 37
2.6.5 Non-Linear Quadratic Linear Matrix Control with State Estimation (NLQDM/SE) 40
2.6.6 Proportional Integral Derivative Controller (PID) 41
2.7 Introduction of Protocol 44
2.8 Protocols 45
11
2.8.1 Intravenous Glucose Tolerance Test (IVGTT) 45
2.8.2 Oral Glucose Tolerance Test (OGTT) 53
2.8.3 Meal Simulation Model (MSM) 58
2.8.4 Computer Based Insulin and Manual Protocol 73
2.9 Critically Ill Patients 77
2.9.1 Intensive Unit Care (ICU) 78
CHAPTER 3 79
METHODOLOGY 79
3.1 Introduction of Statistics 79
3.1 Selective Statistical Analysis 79
3.1.1 Mann-Whitney U Test (MWW U Test) 80
3.1.2 Regression Analysis (Linear Regression) 85
3.1.3 One Way Anaysis of Variance (ANOVA) 89
3.2 Flow Chart 94
CHAPTER 4 95
RESULT 95
4.2 Scatter Plot 95
4.2.1 Scatter Plot of Average Blood Glucose for HTAA and SPRINT Protocols. 97
4.2.2 Scatter Plot of Average Insulin Infusion for HTAA and SPRINT Protocols 103
Table 44 : Insulin Infusion for SPRINT protocol 107
4.3 Histogram 109
4.3.1 Average Blood Glucose Histogram 109
4.3.2 Average Insulin Infusion Histogram 112
4.4 Linear Regression Analysis 115
4.4.1 Linear Regression of Average Blood Glucose Data for HTAA and Christchurch 116
4.4.2 Linear Regression of Average Insulin Infusion Data for HTAA and Christchurch 118
4.5 One Way Analysis of Variance (ANOVA) Table 120
4.5.1 ANOVA Table for Average Blood Glucose 120
4.5.2 ANOVA Table for Average Insulin Infusion 121
CHAPTER 5 122
5.1 Introduction 122
5.2 Recommendation 123
12
REFERENCES 124
APPENDICES 127
13
LIST OF FIGURES
Figure 1: shows the difference between the normal patients, type 1 and type 2 diabetic patients in terms of
insulin secretion 22
Figure 2: shows the flow process of an artificial pancreas consist of glucose sensor, algorithm and insulin
pump for type 1-diabetic patient. 24
Figure 3: shows the flow process the close loop system or the block diagram for the artificial pancreas. 25
Figure 4: shows compartment of glucose and insulin system in a diabetic patient. 27
Figure 5: Shows mixed meal database 60
Figure 6: Shows glucose-insulin control system 61
Figure 7: The unit process model and identification of glucose-insulin subsystem. 67
Figure 8: Unit Process Models 68
Figure 9: Screenshots of computer intravenous insulin therapy protocol. 75
Figure 10: Figure shows the linear regression trend line been generated by using Microsoft Excel 88
Figure 11: Average Blood Glucose upon Patients for HTAA 97
Figure 12: Average Blood Glucose upon Patients for Christchurch 100
Figure 13: Average Insulin Infusion upon Patients for HTAA 103
Figure 14: Average Insulin Infusion upon Patients for Christchurch 106
Figure 15 : Histogram of Average Blood Glucose for HTAA Protocol 110
Figure 16 : Histogram of Average Blood Glucose for SPRINT Protocol 111
Figure 17 : Histogram of Average Insulin Infusion for HTAA Protocol 113
Figure 18 Histogram of Average Insulin Infusion for SPRINT 114
Figure 19 : Regression Graph of Average Blood Glucose Data for HTAA and Christchurch 116
Figure 20 : Regression Graph of Average Insulin Infusion Data for HTAA and Christchurch 118
14
LIST OF TABLES
Table 1: linear approximation parameters 29
Table 2: Impulse response model parameters 29
Table 3: Gaussian White Noise input parameters 30
Table 4: Nth-order discrete modified function 31
Table 5: Laguerre function parameters 33
Table 6: Laguerre coefficient parameters 34
Table 7: Linear MPC parameters 34
Table 8: Nominal value parameters 42
Table 9: PID controllers tuning parameters 43
Table 10: Performance of PID controllers Tuned by 4 methods of the nominal patient case attenuating a
50-g meal disturbance 44
Table 11: Minimal model parameters 46
Table 12: Dynamic model parameters 48
Table 13: IVGTT targeted patients 52
Table 14: Clearance and Insulin concentration parameters 54
Table 15: Change of glucose fluxes and concentration parameters 54
Table 16: Insulin concentration at the site of action respect to plasma insulin parameters 56
Table 17 : Respective OGTT parameters 58
Table 18: OGTT targeted patients 58
Table 19: Glucose subsystem parameters 62
Table 20: Insulin subsystem parameters 63
Table 21: Model parameters of normal and type 2 diabetic patients 65
Table 22 : Insulin Clearance Parameters 66
Table 23: EPG parameters 68
Table 24: Two compartments parameters 68
Table 25: Single compartment parameters 70
Table 26: Insulin in interstitial fluid parameters 71
Table 27: Pancreatic insulin secretion parameters 72
Table 28 : Percentage of blood glucose readings in range for all patients by SICU 77
Table 29: Normal approximation parameters 83
Table 30: Z-table 84
Table 31: Linear Regression Parameters. 86
Table 32: Slope Parameters 86
15
Table 33: X and Y values 87
Table 34: Statistic calculation 87
Table 35: ANOVA table calculation 91
Table 36: Value Substitution in ANOVA table 93
Table 37: F- table 93
Table 38: Blood Glucose Analysis for HTAA protocol 98
Table 39: Outlier Data 98
Table 40: Blood Glucose Analysis for SPRINT Protocol 101
Table 41: Outlier Data 102
Table 42 : Insulin Infusion Analysis for HTAA protocol 104
Table 43 : Outlier Data 105
Table 44 : Insulin Infusion for SPRINT protocol 107
Table 45 : Outlier Data 108
Table 46: Group Data of Average Blood Glucose for HTAA Protocol 109
Table 47 : Group Data of Average Blood Glucose for SPRINT Protocol 111
Table 48: Group Data of Average Insulin Infusion for HTAA Protocol 112
Table 49 : Group Data of Average Insulin Infusion for SPRINT Protocol 114
Table 50 : Summary Output of Average Blood Glucose for HTAA and Christchurch 117
Table 51 : Summary Output of Average Blood Glucose for HTAA and Christchurch 119
Table 52 : ANOVA Analysis for Average Blood Glucose 120
Table 53 : ANOVA Analysis for Average Blood Glucose 121
16
17
CHAPTER 1
INTRODUCTION
1.1 Introduction
Diabetes mellitus is a kind of disease may give a long term effects to the body. Regardless
of races, environmental factors, gender, genetic inheritance, physical conditions, and lifestyles
are taken in account of leading to diabetes mellitus. Diabetes for a long term may lead to other
diseases like kidney malfunction, cardiovascular disease, eye damages, nerve damages, and slow
healing wound. Hence, diabetic patients may suffer from a lot of diseases after a long term
effect. Basically, diabetes mellitus occurs due to destruction of 𝛽-cell which is located in the
pancreas. 𝛽-cell functions as secrete insulin hormone which lowers the blood glucose level.
Excluding normal patients, since they are able to control the blood glucose level naturally, some
special protocols been introduced to the diabetic patients to monitor and control their blood
glucose level from time to time to ensure their safety. Scientific study had proved that extreme
blood glucose level may lead to faint or for the worst case may find glucose content in urine.
Therefore implementing blood glucose control system protocols are necessary as a precautionary
steps and increases alertness among critically-ill patients. In fact, protocols reduce clinical
workload and extreme cost. However, every protocol has been adapted to it algorithm which act
as a controller. Patient’s conditions are considered in every aspect according to the suitability of
each protocol. Studies have shown mortality rate can be reduced by controlling the hyper
18
glycaemia to normal level in Intensive Care Unit (ICU). Malaysia Intensive Care Units uses
Intensive Insulin Therapy (IIT) as current standard protocol. The expected output of this study is
to propose the best protocol for Malaysian patients. In order to propose it, investigation on
different type of blood glucose control system is necessary.
1.2 Problem Statement
It has been found that Malaysia still implement manual protocol among all patients, this
protocol been considered unable to control hyperglycemia situation which cause unexpected
mortality among critically ill patients. It shows that there is lack of technological development of
blood glucose control system protocols in Malaysia. Since there are many advanced protocols
been implemented in western country, it is necessary to propose the suitable protocol that can be
fully automated in order to prevent hyper glycaemia situation and reduces mortality among
critically ill patients. Besides, the proposed protocols may be applicable in labs, clinics or
hospitals which reduce the implemented field workload.
1.3 Objectives
1) To investigate on different types of proposed blood glucose control system.
2) To identify the mathematical model involved in proposed protocols and algorithms.
3) To propose the suitable algorithm and protocol to critically ill patients in Malaysia.
19
1.4 Project Scope
This project targets for Malaysian patients suitability in adapting to proposed blood glucose
control system. This project highlights on protocols, the mathematical model involved among
them, targeted patients for each protocol, algorithm involved in each protocol. As the result,
several statistical analysis method been chosen to outcome with the statement of the suitable
algorithm and protocol for Malaysian patients.
20
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
Different types of blood glucose control system protocols been implemented according to
patients criteria and situation, however the best protocol is important to be fulfill by clinics, labs
and hospitals as there is a number of increase in diabetes mellitus patients due to genetic, ages,
weight and environmental factor. This paper bases on diabetic patient as this project is mainly
focused on investigation on different type of blood glucose control system. Therefore proposes
selective protocols and algorithms that will out come with the most suitable protocol which is
suitable for critically ill patients in Malaysia is the target of the project.
Diabetic patient can be categorized in 2 terms:
a) Type-1 diabetic patient
b) Type-2 diabetic patient
21
2.2 Type of Diabetic Patient
2.2.1 Type-1 Diabetic Patient
Type-1diabetes mainly occurs in new born baby or genetically inherited, where the pancreas
doesn’t produce any insulin to handle glucose level in the blood. These kinds of patients are
recommended to take insulin tablets or for the worst case need to get an insulin injection
(artificial insulin)(Atkinson, Eisenbarth, & Michels, 2014). This type of patients are generally
thought to be precipitated by an immune associated, if not direct immune mediated, destruction
of insulin- pancreatic producing beta cell (β cells)(Atkinson et al., 2014).
2.2.2 Type-2 Diabetic Patient
Type2-diabetes occurs due to bad practice of lifestyle such as imbalanced diet and lack of
exercises. People of type 2-diabetes are able to produce insulin but their body doesn’t use it
correctly. The amount of insulin produced is not enough to control the glucose level in the blood.
Practicing a good lifestyle may control type 2-diabetic patients. Recent meta-analysis provided
evidence that the more amounts of sugar sweetened meals intake are associated with causing of
this type of diabetes. Sucrose contained in sugar –sweetened meals rapidly raises blood glucose
levels(Chung, Oh, & Lee, 2012); this increases the insulin demand and subsequently exhausts
pancreatic β-cells.
22
Figure1: shows the difference between the normal patients, type 1 and type 2 diabetic
patients in terms of insulin secretion
Source: www.endocrineweb.com
2.3 Introduction of Hyperglycemia and Hypoglycemia
2.3.1 Hyperglycemia
Hyperglycemia (> 14 mM glucose concentration) has been associated with the pathogenesis
of vascular complications in diabetes, including the breakdown of the blood retinal
barrier(Losso, Truax, & Richard, 2010). However it doesn’t means a person suffers from
diabetes mellitus with a 100% guarantee. Malfunction of kidney or irregular blood circulatory
system may also lead to hyperglycemia (high blood glucose concentration). Hyperglycemia
mainly occurs when the body has too little insulin production. Insulin plays an important role as
converting glucose in the blood into glycogen. Later the glycogen is stored in liver and will be
released in form of energy during vigorous exercise or activities. High sugar level in urine,
frequent urination, often thirsty shows the symptom of hyperglycemia. Long term complications
23
of hyperglycemia are eye damages, heart attack, nerve damages, kidney damages, strokes and
wound healing problems(Wilson, Richter-Lowney, & Daleke, 1993).
2.3.2 Hypoglycemia
Hypoglycemia (< 3 mM glucose concentration) occurs when the glucose level in the blood
is not enough. High doses of exogenous insulin relative to food and activity cause blood glucose
levels can precipitate hypoglycemia(Turksoy et al., 2013). People who suffer from hypoglycemia
are recommended to take food rich in carbohydrates as their body needs glucose to store the
energy which this energy can be used during vigorous activities. Hyperglycemia may lead to
frequent faint and often tiredness.
2.4 Introduction of Artificial Pancreas
Major improvements in glucose sensing and insulin pumps have led to the practical
feasibility of closed-loop regulatory systems for blood regulations in diabetic patients(Huyett,
Dassau, Zisser, & Doyle, 2015). The development of glucose biosensor technology been
approved by the U.S Food and Drug Administration (FDA). Implantable insulin pump functions
to deliver insulin accurately and safely which has been approved by FDA as well(Huyett et al.,
2015). To complement those improvements in sensing and delivering insulin sort of devices, the
development of an effective control algorithm is necessary and vital(Huyett et al., 2015). The
cost of development and complexity involved in clinically testing control algorithms(Huyett et
al., 2015).
24
Figure 2: shows the flow process of an artificial pancreas consist of glucose sensor,
algorithm and insulin pump for type 1-diabetic patient.
Source: www.telegraph.co.uk
25
2.4.1 Close Loop System for an Artificial Pancreas
Figure 3: shows the flow process the close loop system or the block diagram for the artificial
pancreas.
Source: thedoylgroup.org
This project is based or focused more on the model (mathematical model) and controller
(algorithms) selected to be compared and contrast which is adapted in each protocol proposed in
this project. Each protocol has its own plus points, however it all depends on the patients
situation whether they can adapt to the protocols or not.
2.5 Introduction of Algorithm
Blood glucose can be controlled on a model based algorithm. It utilize variable rate pump in
a closed-loop framework, further improvement in glucose control and normalization of the
glucose distribution in body may be possible(Parker, Doyle III, & Peppas, 1999). As shown in
the previous diagram regarding the artificial pancreas which consists of a glucose biosensor,
26
algorithms and insulin pump. Algorithm is the one act as a controller between the glucose
biosensor and the insulin pump. An implantable glucose concentration sensor(Parker et al., 1999)
would measure diabetic patient blood glucose levels online and eliminate the patient from the
feedback loop(Parker et al., 1999). However, the glucose sensor outcome depends on the
algorithms.
2.6 Algorithms
This project has proposed 5 algorithms to be compared as listed below
1) Input-output control model.
2) Linear model predictive control (Linear MPC).
3) Model predictive control with state estimation (MPC/SE).
4) Non-linear quadratic linear matrix control with state estimation (NLQDMC/SE).
5) Proportional Integral Derivative controller (PID).
2.6.1 Model Based Predictive Control
Model Based Predictive Control (MPC) controller algorithm exhibits a range appropriate
characteristic for the blood glucose control problem and it has been specify into 4 different types
of algorithms.
27
Figure 4: shows compartment of glucose and insulin system in a diabetic patient.
Individual compartment models which has been gained by performing mass balances
around tissues important to glucose or insulin dynamics(Parker et al., 1999). The combined
effects of muscle, adipose tissue and stomach are represented by the periphery in this model, in
gut compartment, the intestine effects were lumped(Parker et al., 1999). The controlled output
for this system is the arterial glucose concentration(Parker et al., 1999), which is regulated by the
manipulating variable insulin infusion rate(Blakemore et al., 2008). This controller is particularly
well suited to the all variable nature of these systems, as well as the inherent constraints involved
in the respective control problem.
2.6.2 Input-Output Controller Model
One of the model predictive controllers utilizes an internal model to estimate the future output
values based on a series of past inputs(Parker et al., 1999). This model form selected for this
work is the linear step-response model.
28
2.6.2.1 Mathematical Model for Input-Output Controller Model
Assumption been done that the system begins at rest, the step-response coefficients, 𝑠(𝑖),
represent the system response to a unit increases in the input variable,
𝑆 = [0𝑠(1)𝑠(2)… 𝑠(𝑀)]𝑇 (1)
M is known as model memory, in the case of the diabetic patients model, the system
approaches steady-state after 180 minutes (1.5% of the total change remaining) and the dynamic
of the response is completed(Parker et al., 1999). For an accurate model, the sampling rate
compulsory to be rapid enough to adequately capture the fastest dynamics of the system(Fisher
& Teo, 1989). A heuristic bound is that the sampling rate should be faster than 20% of the fastest
time constant(Parker et al., 1999). The open loop constant time of the diabetic patient model is
approximately 55 minutes, meaning a sample must be taken at least once every 11 minutes,
fewer parameters make models easier to identify. To simplify the mathematics and decreases the
number of parameters, the chosen sample time is 5 minutes, therefore the model memory, M is
180/5 = 36 sample times(Parker et al., 1999).
Assuming superposition, a linear approximation of the output can be calculated given past
input profile as shown below:
ŷ(𝑘) = ∑𝑠(𝑖)
𝑀
𝑖=1
∆𝑢(𝑘 − 𝑖) + 𝑠(𝑀)𝑢(𝑘 − 𝑀 − 1) (2)
29
The first term represent for the response of the model to the input change over the memory of the
model and the latter term define the steady-state of the process prior to the input change.
Table 1: linear approximation parameters
Variables Defined
ŷ(𝑘) Predicted output value
∆𝑢 Input changes
Step-response coefficients are calculated from an identified impulse-response (IR) model of the
system.
𝑦(𝑘) = ∑ℎ(𝑖)
𝑀
𝑖=1
𝑢(𝑘 − 𝑖) (3)
𝑠(𝑘) = ∑ℎ(𝑖)
𝑀
𝑖=1
(4)
Table 2: Impulse response model parameters
Variables Defined
ℎ(𝑖) Identified impulse response coefficients.
𝑢(𝑘 − 𝑖) Past inputs.
The structure of the impulse-response model in equation (3) is similar to that of the first
order Wiener function and to determine Wiener functional, Gaussian White Noise (GWN) input
sequence are typically used(Parker et al., 1999). But, identification of a physical system model
30
using GWN is not realistic due to the tremendous strain placed on the input regulator. Mean
squared error (MSE) optimal, meaning that it reduces the MSE between the actual output and the
predicted output(Parker et al., 1999). The non-GWN sequence used for diabetic patient model
identification is given by equation (5) and can be treated as a special constant switching pace
symmetric random signal (CSRS)(Parker et al., 1999). In this diabetic patient model, the nominal
insulin delivery rate is 22.33mU/min and the minimum delivery of insulin is 0mU/min which
yields a value 22.33mU/min for B(Parker et al., 1999).
𝑢(𝑘) = 𝐵, 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 1
𝑁𝑃
𝑢(𝑘) = 0, 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑁𝑝 − 2
𝑁𝑃
𝑢(𝑘) = −𝐵, 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 1
𝑁𝑃 (5)
Table 3: Gaussian White Noise input parameters
Variables Defined
𝐵 Maximum symmetric input deviation from its steady state value.
𝑁𝑃 Number of data points in the record.
Accurate parameters identification requires the pulses to be separated by at least points and
the second pulse is the least points M from the end of the data record(Parker et al., 1999). Based
on the earlier choice M = 36, the minimum number points of data required is Np = 74(Parker et
al., 1999). The calculation using the modified Wiener functional method is outlined next(Parker
et al., 1999). Using the CSRS, the Nth-order discrete modified functional as shown below,
31
ŷ(𝑘) = ∑𝑄𝑛
𝑁
𝑛=0
[𝑞𝑛, 𝑢] (6)
Table 4: Nth-order discrete modified function
Variable Defined
𝑄𝑛 Modified Wiener functional
𝑁 Order of the functional used to estimate𝑦
The truncating after the linear terms (N = 1), Qn can be described by the following equations:
𝑄0[𝑞𝑛, 𝑢] = 𝑞0 (7)
𝑄1[𝑞1, 𝑢] = ∑𝑞1
𝑀
𝑖=1
(𝑖)𝑢(𝑘 − 𝑖) (8)
Therefore, in trying to determine the function, from input-output data, the following structure is
utilized:
𝑦(𝑘) = 𝑞0 +∑𝑞1
𝑀
𝑖=1
(𝑖)𝑢(𝑘 − 𝑖) (9)
Restructured to yield:
32
𝑦𝑑(𝑘) =∑𝑞1
𝑀
𝑖=1
(𝑖)𝑢(𝑘 − 𝑖) (10)
Equation (10) results from the knowledge that the zeroth-order modified, q0 is the mean of
ŷ(𝑘)(𝑞0 = 𝐸{𝑦(𝑘)}). Using the description of q0, the output data in deviation form is given by
𝑦𝑑(𝑘) = 𝑦(𝑘) − 𝑞0Error! Bookmark not defined.
The impulse response coefficients, represented by the functional q1 are identified using the
aforementioned cross-correlation method, accounting for the statistical properties of the input
signal through division by the second order moment, m2 equivalent to the variance for the mean-
zero process 𝑦𝑑(𝑘).
Impulse response equation is as shown below,
𝑞1(𝑖) = 𝐸{𝑦𝑑(𝑘)𝑢(𝑘 − 𝑖)}
𝑚2 (11)
Using the cross correlation method, the developed coefficients minimize the prediction error
variance 𝐸{[ŷ(𝑘) − 𝑦(𝑘)]2} between the predicted and the measured output value(Parker et al.,
1999). The impulse-response coefficients are filtered by projection onto Laguerre basis, utilizing
smooth Laguerre functions to approximate the noisy coefficients(Parker et al., 1999). Expansion
of the Laguerre functions returns smooth impulse-response coefficients, which are an optimal
estimate of the noise corrupted coefficients in the MSE sense(Parker et al., 1999).
In discrete time, the jth-order Laguerre function is:
33
𝜙𝑗(𝑖) = √1 − 𝛼2 [∑(−𝛼) (𝑗 − 1
𝑘) (𝑖 + 𝑘 − 1
𝑘 − 1) 𝛼𝑖−𝑗+𝑘𝑈(𝑖 − 𝑗 + 𝑘)
𝑗−1
𝑘=0
] (12)
Table 5: Laguerre function parameters
Variable Defined
𝑈(𝑖 − 𝑗 + 𝑘) Unit step function for 𝑖 = 1,2, … ,𝑀
𝛼 The Laguerre pole, ( 0 <𝛼< 1) determines the rate of exponential
asymptotic decay of the Laguerre functions.
𝜙𝑗(𝑖) Orthonormal in interval of [0,∞)
The least squares generated impulse response coefficients ℎ(𝑖), 𝑖 = 0,1,2, … ,𝑀 satisfying
ℎ(0) = 0 and ∑ ℎ2∞𝑖=0 (𝑖) < ∞ can be represented in:
ℎ(𝑖) = ∑𝑐𝑗
𝐿
𝑗=1
𝜙𝑗(𝑖) (13)
Where L is the number of Laguerre functions chosen to describe the least-squares impulse-
response coefficients and the Laguerre parameters, 𝑐𝑗 are unknowns(Parker et al., 1999). These
Laguerre coefficients are the least-squares solution to:
𝑐𝑗 = (𝜙𝐿𝑇𝜙𝐿)
−1𝜙𝐿𝑇𝐻 (14)
34
Table 6: Laguerre coefficient parameters
Variables Defined
𝐻 = [0ℎ(1)…ℎ(𝑀)]𝑇 The impulse-response coefficient vector.
Φ𝐿 = [ 𝜙1(𝑖)𝜙2(𝑖)𝜙3(𝑖)] Laguerre function matrix.
2.6.3 Linear Model Predictive Control (Linear MPC)
A linear MPC algorithm constructed to control blood glucose concentration based on arterial
glucose sampling and intravenous insulin delivery(Parker et al., 1999).
2.6.3.1 Mathematical Model for Linear MPC
The linear MPC equation is given as:
minΔ𝑈(𝑘) {‖Γ𝑦⌈𝑌(𝑘 + 1|𝑘) − ℛ(𝑘 + 1|𝑘)⌉‖2+ ‖Γ𝑢Δ𝑈(𝑘)‖
2} (15)
Table 7: Linear MPC parameters
Variables Defined
Δ𝑈(𝑘) Future input moves.
ℛ(𝑘 + 1|𝑘) Vector of future reference.
𝑌(𝑘 + 1|𝑘) Vector of predicted future glucose concentrations.
Γ𝑦 Weighting matrices for the set point tracking penalty.
Γ𝑢 Weighting matrices for the insulin move penalty.
(𝑘 + 1|𝑘) Time
35
These two matrices can be used as tuning parameters for the controller, trading off output
performance and manipulated variable movements. Additionally, the input move penalty serves
to regulate the magnitude of noise-induced manipulated variable movement(Parker et al., 1999).
When there is no noise in the diabetic patient simulation, Γ𝑢 is set equal to zero while Γ𝑢 = 1 is
used when band-limited white noise (variance 1.45mg/dl) corrupts the output signal.
The analytical solution involves a multiplication of 𝐾𝑀𝑃𝐶:
𝐾𝑀𝑃𝐶 = [𝐼0…0](𝑆𝑇𝛤𝑦𝑇𝛤𝑦𝑆 + 𝛤𝑢
𝑇𝛤𝑢)−1𝑆𝑇𝛤𝑦
𝑇𝛤𝑦 (16)
Here, the leading vector results from implementing only the one first calculated for ∆𝑈(𝑘).
This demonstrates the ease of implementing linear MPC(Parker et al., 1999). Since the gain
matrix can be pre calculated, the online computation reduces to a simple multiplication.
However, the analytical solution cannot be implemented without accounting for the constraints
present in the system. An input rate constraint ∆𝑈(𝑘) guarantees the pump does not undergo
changes in insulin delivery rate that are greater than mechanism can handle(Parker et al., 1999).
As such, a rate constraint that is conservative with respect to pump dynamics.
The maximum change in insulin delivery rate can be formulated as shown below:
Δ𝑈(𝑘) = 16.5625 𝑚𝑈/min𝑝𝑒𝑟 𝑠𝑎𝑚𝑝𝑙𝑒 (`17)
Since the target is to return the diabetic patient to as normal state as possible, then
maximum insulin delivery rate from the pump should not result in a plasma insulin concentration
in excess if 100mU/l(Parker et al., 1999). It is impossible to remove insulin once it has been
delivered to the patient. Therefore, the input magnitude is constrained as follows:
36
0𝑚𝑈
𝑚𝑖𝑛≤ 𝑈 ≤ 66.25
𝑚𝑈
𝑚𝑖𝑛 (18)
Low blood glucose concentration in the diabetic patients is dangerous and starves the cells
of fuel(Parker et al., 1999). Therefore, an appropriate output constraint is given by:
𝑌(𝑘|𝑘) ≥ 60 𝑚𝑔/𝑑𝑙 (19)
However, the inclusion of hard output constraints in the problem statement can lead to
infeasible programming problems, and will require more computational power that can be
delivered on a digital chip, given current technology, in order to avoid the potential problems
with including an output constraint, it is treated through careful selection of the controller tuning
weights to yield the soft constraint formulation
minΔ𝑈(𝑘) {‖Γ𝑦⌈𝑌(𝑘 + 1|𝑘) − ℛ(𝑘 + 1|𝑘)⌉‖2+ ‖Γ𝑢Δ𝑈(𝑘)‖
2}
Subject to: 0𝑚𝑈
𝑚𝑖𝑛≤ 𝑈 ≤ 66.25
𝑚𝑈
𝑚𝑖𝑛
𝛥𝑈(𝑘)𝑚𝑎𝑥 = 16.5625 𝑚𝑈/min𝑝𝑒𝑟 𝑠𝑎𝑚𝑝𝑙𝑒
𝑚𝑖𝑛{𝑦(𝑘)} ≥ 60 𝑚𝑔/𝑑𝑙
Using the both parameters 𝑚, the move horizon and 𝑝, the prediction horizon, tuning of this
controller been done(Parker et al., 1999). These parameters can be determined by performing a
two-dimensional search over 𝑚 and 𝑝 at the same time the diabetic patient been subjected to an
37
unmeasured disturbance of meal without measurement noise(Parker et al., 1999). The criterion
used to calculate the performance is sum of squared error (SSE) over the time-course of the
simulation, provides the output tracks as the reference. This controller settings minimizing SSE
over the simulation length while eliminating output oscillation are 𝑚 = 2, 𝑝 = 8, Γ𝑦 = 1, and
Γ𝑢 = 0. Using SSE optimal tuning parameters as a starting point, the controller is returned to
accommodate a measurement signal with the noise variance of 1.45mg/dl(Parker et al., 1999).
This returning may be due to violation of the glucose concentration lower bound response to a 50
g oral glucose tolerance test (OGTT). In order to decrease the chatter in manipulated input
signal, the weighting matrices, Γ𝑦 and Γ𝑢 were adjusted until the constraints are satisfied and
chatter in manipulated will be reduced(Parker et al., 1999).
2.6.4 Model Predictive Control with State Estimation (MPC/SE)
MPC/SE shows a slight advantage over MPC, where the increased amount of information
provided to the controller yields tighter control and additional tuning parameters (a Kalman filter
and the reference filter) included to the adjust closed-loop performance(Parker et al., 1999).
38
2.6.4.1 Mathematical Model of MPC/SE
The internal model structure in MPC/SE is changed from the input-output form of equation
(2) to the linear state space form:
��(𝑘 + 1) = 𝜙��(𝑘) + Γ 𝑢(𝑘) (21)
��(𝑘) = 𝐶��(𝑘) (22)
By updating the internal controller model(Parker et al., 1999) with current measurement
information using the Kalman filter, mismatch between the actual patient and the internal model
is significantly decreased(Parker et al., 1999). Hence, the prediction using the updated model is
much more accurate than those of the static input-output model(Parker et al., 1999).
Using the internal model of equations (21) and (22), the controller can estimate the state of
the plant and the output using the following equations:
��(𝑘 + 1) = 𝜙��(𝑘) + Γ 𝑢(𝑘) + 𝒦𝐹[𝑦(𝑘) − 𝐶��(𝑘)] (23)
��(𝑘) = 𝐶��(𝑘) (24)
Formulation of the MPC/SE algorithm utilizes the steady-state Kalman filter, 𝒦𝐹 which is
calculated iteratively off line to minimize controller algorithm computation requirements as:
39
𝒦𝐹(𝑖) = ΦP(i)𝐶𝑇(𝐶𝑃(𝑖)𝐶𝑇 + 𝑅2)−1 (25)
𝑃(𝑖 + 1) = ΦP(i)Φ𝑇 + 𝑅1 −𝒦𝐹(𝑖)𝐶𝑃(𝑖)Φ𝑇 (26)
The initial state covariance matrix 𝑃(0) = {𝑥(0) − ��(0), 𝑥(0) − ��(0)} is the expected
value of the squared initial deviation between the actual state and the best linear estimate of that
state(Parker et al., 1999). The matrix 𝑃(0) = 𝐼 is chosen to represent an initial uncertainty of
1mg/dl in the glucose concentration or 1mU/l in the insulin concentration satisfies the
requirement of 𝑃(0) > 0. The measurement noise covariance matrix 𝑅2 is the dependent on the
statistical measurement noise. When incorporated, the band-limited white noise with power =
0.1, gain = 0.85mg/dl and sample time equal to 0.05 min, corrupts the glucose measurement
signal(Parker et al., 1999). These noise characteristic define a close white sequence with mean 0
mg/dl and maximum deviation of 5mg/dl yielding R2= 1.45. The third parameter of the steady
state Kalman filter is 1, the process noise covariance matrix. The element R1 is weighted
according to relative importance in detecting a glucose meal disturbance(Parker et al., 1999). The
glucose states will vary more significantly than insulin, auxiliary, or glucagon equation states,
hence larger weights are used for those elements(Heinonen & Mäkipää, 2002). Knowledge of the
mismatch between the linear internal model and the actual nonlinear model of the diabetic
patient is also taken in account(Heinonen & Mäkipää, 2002).
𝑅1 = 𝑑𝑖𝑎𝑔[0.1 ∗ 𝑂(8), 0.01 ∗ 𝑂(9), 1, 1] (27)
Where 𝑂(𝑛) is an 𝑛 −length vector, the problem now reduces to tuning controller. A 3-
dimensional search is performed over 𝑚, 𝑝 and the reference filter Φ𝑟, such that sum-squared
error is minimized and constraints are satisfied(Parker et al., 1999). By utilizing the Kalman
filter in the controller, a more aggressive formulation with 𝑝 = 7 is possible taking Φ𝑟 = 0.65.
40
For accounting the measurement noise, the controller is detuned by increasing the prediction
horizon to 𝑝 = 8 as well as tune back the R1 matrix such that all weights are < 1.0 yielding:
𝑅1 = 𝑑𝑖𝑎𝑔[0.1 ∗ 𝑂(8), 0.01 ∗ 𝑂(9), 0.1, 0.1] (28)
2.6.5 Non-Linear Quadratic Linear Matrix Control with State Estimation
(NLQDM/SE)
NLQDMC/SE is an alternate controller which takes greater advantages of the nonlinear
model of the diabetic patient(Parker et al., 1999). This is a logical extension of linear MPC with
the state estimation with compensation for known nonlinearity of the controlled process.
NLQDMC/SE plus point on nonlinear model once more during the controller computational
sequences(Parker et al., 1999). When calculating the effects of the past inputs on the output
prediction in NLQDMC/SE, nonlinear model is used to place of the linear discrete model(Parker
et al., 1999). The estimation of the future plant states given the current information including the
newly calculated insulin delivery rate accomplished through integration of the nonlinear model
updated by the correction term 𝜅𝐹[𝑦(𝑘) − 𝐶��(𝑘)]. Therefore it requires the solution of only
one quadratic programming problem online(Parker et al., 1999). The sum of the linear and
nonlinear effects were then used to calculate the vector of the future input moves necessary to
drive the system to track the reference value(Parker et al., 1999).
The criterion is to minimize the sum squared error over the time course of simulation(Parker
et al., 1999). Under noise-free conditions, the resulting parameters are m = 2, 𝑝 = 5, and
Φ𝑟 = 0.57. Similar to MPC/SE, the weighting matrix values are Γ𝑦 = 1 and Γ𝑢 = 0.
41
2.6.6 Proportional Integral Derivative Controller (PID)
The PID controllers are assessed with a detailed physiological model of diabetic patients for
their ability to reject meal disturbance and their robustness in the presence of parametric which is
not certain(Ramprasad, Rangaiah, & Lakshminarayanan, 2004). One of the recently developed
PID tuning techniques is able to maintain the glucose concentration(Ramprasad et al., 2004)
above the hypoglycemic range (<60mg/dL) in 95% and 100% with fine tuning has been tested on
577 diabetic patients, while rejecting both single and multiple meal disturbance(Ramprasad et
al., 2004).
PID controller has been the workhorse for regulatory control in the chemical and process
industries(Ramprasad et al., 2004). It is a simple structure and effective in a wide range of
industrial process as well as accumulated experienced in its design, making it an extreme
attractive biomedical application(Huyett et al., 2015). In present case study, the PID controller is
designed for the model using both classical and tuning methods. The PID controller is tuned with
integral of absolute error (IAE) minimization (for disturbance rejection), then Cohen-Coon
tuning followed by Shen method and DCM based method(Ramprasad et al., 2004). The resulting
PID controllers are assessed for their ability to detect normoglycemia set point in a diabetic
while subjected to a 50g meal disturbance. It is tested on 577 patients on both single meal and
multiple meals (in a day) are considered as the disturbance for blood glucose control(Ramprasad
et al., 2004).
2.6.6.1 Mathematical Model of PID Controller
The diabetic model involved in PID controller is known as nonlinear
pharmacokinetic/pharmacodynamics compartment model(Ramprasad et al., 2004). The model
been created to represent a 70-kg male patient, it has 2 inputs, insulin delivery and meal
disturbance and 1 output, blood glucose concentration. The insulin delivery rate represent as a
42
deviation from 22.3mU/min nominal value(Ramprasad et al., 2004). The meal disturbance has a
nominal value of 0 mg/min (absorption into the blood stream)(Ramprasad et al., 2004).The blood
glucose concentration from the nominal value of 81.1mg/dl(Ramprasad et al., 2004). Below
represent the equation for these variables:
𝑚𝑑 =1
360��𝑑 , 𝑢 =
1
33.125��, 𝑌 =
1
20�� (29)
Table 8: Nominal value parameters
Variables Defined
��𝑑 Meal disturbance.
�� Insulin delivery rate.
�� Blood glucose concentration.
𝑢 Maximum insulin delivery rate.
𝑌 Scaled plasma glucose deviation.
The glucose and insulin dynamics(Ramprasad et al., 2004) were found to be most sensitive to
variations in the metabolic parameters of the liver and the periphery(Ramprasad et al., 2004). In
patient model, the glucose metabolism is mathematically described by the following general
structure:
𝛤𝑒 = 𝐸𝛤𝑒{𝐴𝛤𝑒 − 𝐵𝑟 tanh[𝐶𝛤𝑒(𝑥𝑖 + 𝐷𝛤𝑒)]} (30)
The subscript 𝑖 in (2) is the state vector element involved in the metabolic effect and ‘e’
denoted specific effects within the model: the effect of glucose on hepatic glucose production
(EGHGP), the effect of glucose on hepatic glucose(Ramprasad et al., 2004) uptake (EGHGU)
43
and the effect of insulin on peripheral(Ramprasad et al., 2004) glucose uptake
(EIPGU)(Ramprasad et al., 2004). Inter- or intra patient uncertainty were classified
physiologically as either a receptor 𝐷Γ𝑒 and or a post receptor 𝐸Γ𝑒. These 2 parameters were
estimate to fit the actual patient data. Differences in insulin clearance between patients also exist
and were modeled as deviations in fraction of clearance by a given compartment like fraction of
hepatic clearance (FHIC) or the fraction of peripheral insulin clearance (FPIC)(Ramprasad et al.,
2004). This uncertainty formulation essentially focuses on liver, peripheral (muscle/fat), and
tissues considered more relevant in the case study.
Patient models were assumed to capture all inter and intra patient variability among type 1
diabetic case(Balakrishnan, Rangaiah, & Samavedham, 2011). Each of these patients models was
subjected to a 50g meal disturbance at time t = 0, under closed loop conditions to test the
robustness and disturbance-attenuating capabilities of the designed controller(Ramprasad et al.,
2004).
PID controller tuning has the form of:
𝑢(𝑡) = 𝐾𝑝𝑒(𝑡) + 𝐾𝐼∫𝑒(𝑡)𝑑𝑡 + 𝐾𝐷𝑑𝑒(𝑡)
𝑑𝑡 (31)
Where 𝑒(𝑡) = 𝑌𝑠𝑝(𝑡) − 𝑌(𝑡), 𝑌𝑠𝑝(𝑡) = 0 as the set point.
Table 9: PID controllers tuning parameters
Variables Defined
𝑢(𝑡) Controller output.
𝑒(𝑡) Error.
𝑌(𝑡) Scaled plasma glucose concentration.
𝐾𝑝,𝐾𝐷 , 𝐾𝐼 Relative weights of proportional, integral, and
derivative components respectively of the control
action.
44
There are 4 types of tuning method available for PID controller:
1) Integral of Absolute Error (IAE).
2) Dynamic Matrix Control (DMC).
3) Cohen-Coon.
4) Shen method.
Table 10: Performance of PID controllers Tuned by 4 methods of the nominal patient
case attenuating a 50-g meal disturbance
Source:
2.7 Introduction of Protocol
Protocol is a plan for a scientific experiment or medical treatment(Blaha et al., 2009). Blood
glucose control protocol has been developed to provide direction and guidance through services
are expected to manage the risk associated with the process of clinical testing in response to the
changing nature of health care provision for the people with diabetes mellitus.
45
2.8 Protocols
This project has proposed 4 protocols to be compared as list below
1) Intravenous Glucose Tolerance Test (IVGTT)
2) Oral Glucose Tolerance Test (OGTT)
3) Meal Simulation Model (MSM)
4) Computer Based Insulin Infusion (CBII)
2.8.1 Intravenous Glucose Tolerance Test (IVGTT)
IVGTT is a tool for the assessment of insulin sensitivity(Fang, Shi, Sun, & Fang, 1997) and
𝛽 − 𝑐𝑒𝑙𝑙 function in diabetic research and perioperative studies(Fang et al., 1997). A bolus
injection of glucose is given and the plasma concentration insulin and glucose are usually
measured in 3 hours. IVGTT requires frequent blood sampling and is labor intensive. IVGTT
uses proportional integral device (PID) controller as the algorithm(Fang et al., 1997).
The minimal model, which is currently used in physiological research on the metabolism of
glucose, was proposed for the interpretation of the glucose insulin plasma concentration
following the IVGTT which is consists of 2 parts(De Gaetano & Arino, 2000).
1st part consists of two differential equations and describes the glucose plasma concentration
time-course treating insulin plasma(De Gaetano & Arino, 2000) concentration as a known
forcing function. The 2nd
part consists of a single equation and describes the time course(De
Gaetano & Arino, 2000) of plasma insulin concentration treating glucose plasma concentration
as a known forcing function(De Gaetano & Arino, 2000). A simple delay-differential model is
introduced and demonstrated to be globally asymptotically stable around a unique
equilibrium(De Gaetano & Arino, 2000) point corresponding to pre-bolus conditions(De
Gaetano & Arino, 2000).
46
2.8.1.1 Mathematical Model of IVGTT
The physiological experiment consist in the injecting into the bloodstream of the
experimental subject a bolus of glucose, thus inducing an (impulse) increase in the plasma
glucose concentration 𝐺(𝑡) and a corresponding increase of the plasma concentration of insulin
𝐼(𝑡), secreted by the insulin(De Gaetano & Arino, 2000). The concentration is measured between
3 hours interval time beginning at injection(De Gaetano & Arino, 2000).
The standard formulation of the minimal model as shown below:
𝑑𝐺(𝑡)
𝑑𝑡= −[𝑝1 + 𝑋(𝑡)]𝐺(𝑡) + 𝑝1𝐺𝑏 , 𝐺(0) = 𝑝0 (32)
𝑑𝑋(𝑡)
𝑑𝑡= −𝑝2𝑋(𝑡) + 𝑝3[𝐼(𝑡) − 𝐼𝑏], 𝑋(0) = 0 (33)
𝑑𝐼(𝑡)
𝑑𝑡= 𝑝4[𝐺(𝑡) − 𝑝5] + 𝑡 − 𝑝6[𝐼(𝑡) − 𝐼𝑏], 𝐼(0) = 𝑝7 + 𝐼𝑏 (34)
We may define the following parameters for minimal model as shown below,
Table 11: Minimal model parameters
Variables Defined
𝐺(𝑡) [mg/dl] The blood glucose concentration at time t [min].
𝐼(𝑡) [µUI/ml] The blood insulin concentration.
𝑋(𝑡) [min-1
] An auxiliary function representing insulin-excitable tissue
47
glucose uptake activity, proportional to insulin
concentration in a “distance” compartment.
𝐺b [mg/dl] The subject's baseline glycaemia.
𝐼b [µUI/ml] The subject's baseline insulinemia.
𝑝0 [mg/dl] The theoretical glycaemia at time 0 after the instantaneous
glucose bolus.
𝑝1 [min-1
] The glucose “mass action” rate constant, i.e. the insulin-
independent rate constant of tissue glucose uptake, “glucose
effectiveness”.
𝑝2 [min-1
] The rate constant expressing the spontaneous decrease of
tissue glucose uptake ability.
𝑝3 [min-2
(µUI/ml)-1
] The insulin-dependent increase in tissue glucose uptake
ability, per unit of insulin concentration excess over baseline
insulin.
𝑝4 [(µUI/ml) (mg/dl)-1
min-1
]
The rate of pancreatic release of insulin after the bolus, per
minute and per mg/dl of glucose concentration above the
“target” glycemia”.
𝑝5 [mg/dl] The pancreatic “target glycemia''
𝑝6 [min-1
] The first order decay rate constant for Insulin in plasma.
𝑝7 [µUI/ml] The theoretical plasma insulin concentration at time 0,
above basal insulinemia, immediately after the glucose
bolus.
The coupled minimal model difficulties have been overcome by alternative model for
glucose-insulin system which has been proposed.
The dynamic model of the glucose-insulin system been introduced and studied is as shown
below,
𝑑𝐺(𝑡)
𝑑𝑡= −𝑏1𝐺(𝑡) − 𝑏4𝐼(𝑡)𝐺(𝑡) + 𝑏7 (35)
𝐺(𝑡) ≡ 𝐺𝑏∀𝑡 ∈ [ −𝑏5, 0), 𝐺(0) = 𝐺𝑏 + 𝑏0 (36)
𝑑𝐼(𝑡)
𝑑𝑡= −𝑏2𝐼(𝑡) +
𝑏6𝑏5∫ 𝐺(𝑠) 𝑑𝑠,𝑡
𝑡−𝑏5
𝐼(0) = 𝐼𝑏 + 𝑏3𝑏0 (37)
48
We may define the following parameters regarding dynamic model as shown below,
Table 12: Dynamic model parameters
Variables Defined
𝑡 [min] Time.
𝐺[mg/dl] The glucose plasma concentration.
𝐺b[mg/dl] The basal (pre injection) plasma glucose concentration.
𝐼 [pM] The insulin plasma concentration.
𝐼b[pM] The basal (pre injection) insulin plasma concentration.
𝑏0 [mg/dl] The theoretical increase in plasma concentration over
basal glucose concentration at time zero after instantaneous
administration and redistribution of the I.V. glucose bolus.
𝑏1 [min-1
] The spontaneous glucose first order disappearance rate
Constant.
𝑏2 [min-1
] The apparent first-order disappearance rate constant for insulin.
𝑏3 [pM/(mg/dl)] The first-phase insulin concentration increase per (mg/dl)
increase in the concentration of glucose at time zero due to
the injected bolus.
𝑏4 [min-1
pM-1
] The constant amount of insulin-dependent glucose
disappearance rate constant per pM of plasma insulin
concentration.
𝑏5 [min] The length of the past period whose plasma glucose concentrations
influence the current pancreatic insulin secretion.
𝑏6 [min-1
pM/(mg/dl)] The constant amount of second-phase insulin release rate per
(mg/dl) of average plasma glucose concentration throughout the
previous b5minutes.
𝑏7[(mg/dl) min-1
] The constant increase in plasma glucose concentration due to
constant baseline liver glucose release.
Model above describes glucose concentration changes in blood as depending on
spontaneous, insulin-independent net glucose tissues uptake, on insulin-dependent net glucose
tissue uptake and on constant baseline liver glucose production(De Gaetano & Arino, 2000). The
term net glucose uptake shows that changes in tissue glucose uptake and in liver glucose delivery
are considered together. Insulin Plasma concentration changes were considered to depend on the
spontaneous constant rate decay, this because of the secretion of insulin by pancreas and insulin
catabolism(De Gaetano & Arino, 2000). The delay terms refers to the pancreatic secretion of
insulin: effective pancreatic secretion(De Gaetano & Arino, 2000)after the liver first pass effect)
when time t is to be proportional to the average value of glucose concentration(De Gaetano &
49
Arino, 2000) in the 𝑏5 minutes preceding time t(De Gaetano & Arino, 2000). The effect of delay,
as initial conditions for the problem that have to specify not only the glucose level at time zero,
but also the value at times from 𝑏5 to 0. The term (1/𝑏5) in front of the integral in Eq. (5) has
been introduced to make the integral equal one for constant unit glucose concentration(De
Gaetano & Arino, 2000), thus making 𝑏6, pancreatic response, independent of 𝑏5, the period of
time for pancreatic sensitivity to plasma glucose concentrations(De Gaetano & Arino, 2000).
The free parameters are only 6 (𝑏0 through 𝑏5). Assuming the subject is at equilibrium at (𝐺b, 𝐼b)
for a sufficient long time (>𝑏5) prior to the administration of the bolus, then:
0 = −𝑏1𝐺𝑏 − 𝑏4𝐼𝑏𝐺𝑏 + 𝑏7& 0 = −𝑏2𝐼𝑏 + 𝑏6𝐺𝑏
Equate together, hence
𝑏7 = 𝑏1𝐺𝑏 + 𝑏4𝐼𝑏𝐺𝑏 , 𝑏6 = 𝑏2𝐼𝑏𝐺𝑏
For model fitting, observations have been weighted according to the usual IVGTT scheme
glucose observations before 8 minutes have been given a weight of zero (assumption of glucose
bolus distribution to be complete by 8 minutes), and insulin observations before the first insulin
peak (average 2 or 4 minutes) have also been given a weight of zero(De Gaetano & Arino,
2000). No points have been over weighted (all points have weight either zero or one). Parameters
values were obtained by weighted least squares using a quasi-Newton minimization(De Gaetano
& Arino, 2000) algorithm. Minimal model study, 𝑝5is the target glycemia which the pancreatic
secretion of insulin attempts to attain(De Gaetano & Arino, 2000) (above which the pancreas is
assumed to secrete the glycemia-lowering hormone insulin)whereas 𝐺b is the measured baseline
glycemia(De Gaetano & Arino, 2000), results from the equilibrium between the pancreatic action
to lower glycemia down to 𝑝5 and the endogenous (liver)(De Gaetano & Arino, 2000) glucose
50
production tends to raise glycemia. In general, 𝐺b may be greater than 𝑝5, and this is in fact the
case(De Gaetano & Arino, 2000) in where the program to estimate the parameters of the minimal
model is described in the reported to be𝐺b=92 mg/dl, 𝑝5=89.5 mg/dl(De Gaetano & Arino,
2000).
Proposition I.1 refers to the case in which glycemia(De Gaetano & Arino, 2000), 𝐺(𝑡)
returns tobasal 𝐺𝑏 after the metabolization of the glucose bolus(De Gaetano & Arino, 2000).
Suppose 𝐺𝑏 > 𝑝5, lim sup t →∞𝐺(𝑡) < 𝑝5, then lim sup t → ∞ 𝑋(𝑡) = ∞
Proposition I.2 refers to the case in which glycemia tends to drop below the pancreatic(De
Gaetano & Arino, 2000) target level p5(De Gaetano & Arino, 2000). Suppose lim sup t → ∞
𝐺(𝑡) < 𝑝5, then 𝐺𝑏 ≤ 𝑝5.
Proposition I.3, The two propositions above leave open the possibility that the upper limit of
glycemia, t increases, exactly equals 𝑝5(De Gaetano & Arino, 2000). The analysis of this
boundary case is not easy: however, either one of the two above cases would be produced for
arbitrarily small changes in the p5(De Gaetano & Arino, 2000) parameter.
Proposition I.4, for any value 𝑝5 < 𝐺𝑏the system doesn’t admit equilibrium(De Gaetano &
Arino, 2000). Proposition I.5, if the subject is considered to be at steady state before the glucose
bolus, then 𝐺𝑏 must be lesser than or equal to 𝑝5.
In fact, p5 is the unknown but true value of a model parameter(De Gaetano & Arino, 2000),
while 𝐺b is a measured quantity equal to the sum of the true unknown value of the pre-injection
equilibrium state(De Gaetano & Arino, 2000) plus some (observation) error(De Gaetano &
Arino, 2000). In any case, it is interesting to note that, in the case where 𝑝5= 𝐺b, the possible
solutions(De Gaetano & Arino, 2000), which start out at a greater value than 𝐺b (due to the bolus
injection of glucose) are forced to pass below the 𝐺b level(De Gaetano & Arino, 2000) before
they can converge to 𝐺b, and once they pass below this value, can never cross it again to become
greater than 𝐺b(De Gaetano & Arino, 2000). In other words, it is not possible for a solution to converge to
𝐺b to oscillate in any way (damped or otherwise) around 𝐺b(De Gaetano & Arino, 2000).
51
Proposition I.6, let 𝑝3 > 0, 𝑝5 = 𝐺𝑏 , 𝐺(0) > 𝐺𝑏, assume 𝐺(𝑡), 𝑋(𝑡)bounded, then there
exist 𝑇 > 0 such that 𝐺(𝑡) > 𝐺𝑏 for all 𝑡 < 𝑇, 𝐺(𝑇) = 𝐺𝑏 and 𝐺(𝑡) < 𝐺𝑏 for all 𝑡 >
𝑇Error! Bookmark not defined.
Stability of dynamic model, It can be shown that the dynamical model admits one and only
one equilibrium point with positive concentrations, (Gb, Ib )(De Gaetano & Arino, 2000).
Proposition II.3, the function{𝐺(𝑡), 𝐼 (𝑡)} are positive and bounded(De Gaetano & Arino, 2000).
Proposition II.4, the time derivatives of the solutions are bounded(De Gaetano & Arino, 2000).
52
2.8.1.2 IVGTT Targeted Patients
Table 13: IVGTT targeted patients
53
2.8.2 Oral Glucose Tolerance Test (OGTT)
Oral Glucose Tolerance Test (OGTT) provides information(Mari, Pacini, Murphy, Ludvik,
& Nolan, 2001)on insulin secretion and action but does not directly yield a measure of insulin
sensitivity. Oral glucose tolerance test, standard3-h 75-g OGTT was performed. Blood samples
collected at 0, 30, 60, 90,120, and 180 minutes(Mari et al., 2001) for the measurement of insulin
and plasma glucose(Mari et al., 2001). A loading dose of insulin was administered in a
logarithmically decreasing(Mari et al., 2001) manner over a 10 minutes time, next constant
infusion rate of 120 mU min-1
min-2
for next 240 minutes(Mari et al., 2001). Nowadays, OGTT
method for assessing insulin sensitivity is based on an equation that predicts glucose clearance
during a hyperinsulinemic-euglycemic(Mari et al., 2001) clamp using the values of glucose and
insulin concentration obtained from an OGTT. The equation is derived from a model(Mari et al.,
2001) of the glucose-insulin relationship, which although simplified, is based on established
principles of glucose kinetics(Mari et al., 2001) and insulin action(Mari et al., 2001). The model
derived equation requires the knowledge of parameters that cannot be directly calculated(Mari et
al., 2001) from an OGTT(Stumvoll, Van Haeften, Fritsche, & Gerich, 2001). This protocol uses
model predictive control (MPC) controller as the algorithm(Parker et al., 1999).
2.8.2.1 Mathematical Model of OGTT
Model equations, assume that connections between glucose clearance and insulin
concentration as a linear equation shown below:
𝐶𝑙 = 𝐶𝑙𝑏 + 𝑆∆𝐼 (38)
54
Table 14: Clearance and Insulin concentration parameters
Variables Defined
𝐶𝑙 (ml min-1
m-2
) Glucose clearance.
𝐶𝑙𝑏 (ml min-1
m-2
) Basal glucose clearance.
∆𝐼(µU/ml) Increment over basal insulin concentration.
𝑆[(ml min-1
m-2
)/(µU/ml)] Slope of the line.
Equation (1) represents the relationship according to experiment observed when the
concentration of insulin is in the physiological range(Mari et al., 2001). Equation (1) is the
predictor of glucose clearance at reference insulin concentration increment. Glucose kinetic
during the OGTT with single compartment model is a reasonable simplification in the OGTT
because changes of glucose fluxes and concentration are gradual(Mari et al., 2001). The model is
described by the differential equation:
𝑉𝑑𝐺(𝑡)
𝑑𝑡= −𝐶𝑙(𝑡)𝐺(𝑡) + 𝑅𝑎(𝑡) (39)
Table 15: Change of glucose fluxes and concentration parameters
Variables Defined
𝑉 (ml/m2) Glucose distribution volume.
𝐺(t) (mg/ml) Glucose concentration.
𝑅𝑎 (mg min-1
) Glucose rate of appearance.
For V, cannot determine from OGTT, hence, need to assume 10 l/m2 which represent total
glucose distribution volume(Mari et al., 2001). The initial steady state condition for equation (2)
represent G(0) = Ra(0)Cl(0) when time is 0 then that is the basal value(Mari et al., 2001).
55
Assume Cl(t) in equation (2) and equation (1) are related insulin concentration increment, in
a compartment remote from plasma, hence:
𝑉𝑑𝐺(𝑡)
𝑑𝑡= −[𝐶𝑙𝑏 + 𝑆∆𝐼]𝐺(𝑡) + 𝑅𝑎(𝑡) (40)
Equation (3) can be solved for S, treating other variables as known, S obtained can be
inserted into equation (1) because 𝐶𝑙𝑏 = 𝑃𝑏/𝐺𝑏 where 𝑃𝑏 is the basal production(Mari et al.,
2001). The equation of predicting glucose clearance at the target insulin concentration increment
as shown below:
𝐶𝑙 =∆𝐼
∆𝐼𝑟(𝑡)[𝑅𝑎(𝑡) −
𝑉𝑑𝐺(𝑡)
𝑑𝑡
𝐺(𝑡)+𝑃𝑏 (
∆𝐼𝑟(𝑡)
∆𝐼− 1)
𝐺𝑏 (41)
When evaluated t = 120 minutes hence 𝐺(120), 𝐺𝑏(120)/𝑑𝑡, 𝑅𝑎(120), ∆Ir(120), glucose
concentration exhibits down slope from the derivation of glucose concentration, 𝑑𝐺(𝑡)/𝑑𝑡 as
[𝐺(180) − 𝐺(120)]/60, 𝑅𝑎(120) is expected to depend on oral glucose dose(Mari et al., 2001).
Assume 𝑅𝑎(120) is a constant fraction, of oral glucose dose , D0 (in g/m2), hence ∆𝐼𝑟(120)
can be calculated as shown below:
∆𝐼𝑟(120) = 𝐼(120) − 𝐼(0) + 𝑝2 (42)
56
Table 16: Insulin concentration at the site of action respect to plasma insulin parameters
Variables Defined
𝐼(µU/ml) Insulin concentration
∆𝐼𝑟 Insulin concentration at the site of action respect to plasma insulin.
𝑝2 Parameter
𝑝2 parameter being introduced to prevent ∆𝐼𝑟(120) from assuming near zero values when the
insulin secretary is low. The second fraction in equation (4) is modified as shown below:
𝑃𝑏(∆𝐼𝑟(𝑡)
∆𝐼−1)
𝐺𝑏=
𝑝3𝐺(0)
(43)
𝑝3 is another parameter, this expression is due to an effective way to formulate basal
production, Pb to the limitation of predictor ∆𝐼𝑟. Glucose clearance does not depend on glucose
concentration(Mari et al., 2001).
To obtain the prediction of glucose clearance at euglycemia, correction for the glycemia
level was introduced. Ratio between the clamp glucose clearance at euglycemia 𝐶𝑙𝐸𝑈(Mari et al.,
2001) and glucose clearance calculated from OGTT 𝐶𝑙𝑂𝐺𝑇𝑇 is:
𝐶𝑙𝐸𝑈𝐶𝑙𝑂𝐺𝑇𝑇
= 𝑝5 (1 +𝑝6𝐶𝑙𝐸𝑈
) [𝐺(120) − 𝐺𝐶𝐿𝐴𝑀𝑃] + 1 (44)
57
𝐺𝐶𝐿𝐴𝑀𝑃 is the clamp glucose concentration normally 90 mg/dl(Mari et al., 2001), G(120)
represent average glucose concentration during OGTT while p5 and p6 are parameters. In
equation 7, glucose clearance decreases with increasing glucose concentration (the ratio of clamp
to OGTT clearance increases linearly(Mari et al., 2001) as the glucose concentration during
OGTT increase)(Mari et al., 2001).
Where the equation of 𝐶𝑙𝑂𝐺𝑇𝑇 and 𝐶𝑙𝐸𝑈 are shown below:
𝐶𝑙𝑂𝐺𝑇𝑇 =
𝑝1𝐷0−𝑉[𝐺(180)−𝐺(120)]/60
𝐺(120)+𝑝3𝑝4
𝐺(0)
𝐼(120) − 𝐼(0) + 𝑝2
𝐵 = [𝑝5(𝐺(120) − 𝐺𝐶𝐿𝐴𝑀𝑃) + 1]𝐶𝑙𝑂𝐺𝑇𝑇
𝐶𝑙𝐸𝑈 =1
2[𝐵 + √𝐵2 + 4𝑝5𝑝6(𝐺(120) − 𝐺𝐶𝐿𝐴𝑀𝑃)𝐶𝑙𝑂𝐺𝑇𝑇] (45)
Equation (8) require oral dose D0, glucose concentration value G(0), G(120) and G(180)
and insulin concentration I(0) and I(120). Table below shows GCLAMP, V and parameters p1 until
p6(Mari et al., 2001).
58
Table 17 : Respective OGTT parameters
Evaluation of β-cell function, strongly related to insulin sensitivity with clamp and OGTT,
calculation of simple index β-cell function as the ratio between area under insulin increment in
insulin concentration and the area under increment during OGTT(Mari et al., 2001).
2.8.2.2 OGTT Targeted Patients
Table 18: OGTT targeted patients
2.8.3 Meal Simulation Model (MSM)
Simulation meal model of the glucose insulin control system(Man, Rizza, & Cobelli, 2007)
during meals and normal daily life is highly desirable for the study of pathophysiology of
59
diabetes and for the evaluation of glucose sensor, insulin infusion algorithms and decision to
support treatment of diabetes(Man et al., 2007)focusing type 1 diabetic patients(Man et al.,
2007). This simulation model of glucose insulin system can describe the physiological events
occur during the intake of meal. The new venture is a unique set of data for 204 normal
individuals (without any disease) who were underwent a triple tracer meal protocols, model-
independent fashion, time course of all the relevant glucose and insulin fluxes(Man et al., 2007)
during meal. Glucose-insulin system were model or portrait as “concentration and flux” by
sorting to a subsystem forcing function strategy. This model is also suitable for type 2 diabetic
patients. Meal Simulation Model (MSM) uses Model Predictive Control (MPC) controller as
algorithm(Palti, 1992).
60
Figure 5: Shows mixed meal database
According to the model, a scheme of the glucose-insulin system control system which puts
in relation the measured plasma concentration example glucose G and insulin I and the glucose
fluxes example rate of appearance Ra, production EGP, utilization U, renal extraction E and
insulin fluxes(Man et al., 2007) example secretion S, and degradation D as shown in figure 1
above(Man et al., 2007).
Figure 2 shows the complexity of the system, the availability of plasma glucose and insulin
concentration makes it virtually impossible to build a reliable simulation(Man et al., 2007)
model.
61
Figure 6: Shows glucose-insulin control system
62
2.8.3.1 Mathematical Model of MSM
The model equations for glucose subsystem are shown as below:
{
��𝑝(𝑡) = 𝐸𝐺𝑃(𝑡) + 𝑅𝑎(𝑡) − 𝑈𝑖𝑖(𝑡) − 𝐸(𝑡) − 𝑘1. 𝐺𝑝(𝑡) + 𝑘2. 𝐺𝑡(𝑡) 𝐺𝑝(0) = 𝐺𝑝𝑏
��𝑡(𝑡) = −𝑈𝑖𝑑(𝑡) + 𝑘1. ��𝑝(𝑡) − 𝑘2. 𝐺𝑡(𝑡) 𝐺𝑡(0) = 𝐺𝑡𝑏
𝐺(𝑡) =𝐺𝑝
𝑉𝐺 𝐺(0) = 𝐺𝑏
(46)
Table 19: Glucose subsystem parameters
Variables Defined
𝐺𝑝𝑎𝑛𝑑 𝐺𝑡(mg/kg) Glucose mass in plasma, rapidly and slowly equilibrating tissues.
𝐺(mg/dl) Glucose concentration.
𝐸𝐺𝑃(mg/kg/min) Endogenous glucose production.
𝑅𝑎(mg/kg/min) Glucose rate appearance in plasma.
𝐸(mg/kg/min) Renal excretion.
𝑏 Denotes basal state.
𝑈𝑖𝑖 Insulin dependent utilization.
𝑈𝑖𝑑 Glucose dependent utilization.
𝑘1 𝑎𝑛𝑑 𝑘2(min-1
) Rate parameters.
𝑉𝐺(dl/kg) Distribution volume of glucose.
In basal state endogenous production, 𝐸𝐺𝑃𝑏 equals to the glucose disappearance which
equals to the summation of glucose utilization and renal excretion( zero for normal subject),
𝑈𝑏 + 𝐸𝑏(Man et al., 2007).
𝐸𝐺𝑃𝑏 = 𝑈𝑏 + 𝐸𝑏 (47)
63
Parameters 𝑉𝐺, 𝑘1 𝑎𝑛𝑑 𝑘2 are for both normal and type 2 diabetic patient(Man et al., 2007).
In insulin subsystem, there are 2 compartments describe insulin kinetics as shown in figure
3(Man et al., 2007). The model equations for the insulin subsystem are shown below:
{
𝐼��(𝑡) = −(𝑚1 +𝑚3(𝑡)). 𝐼𝑡(𝑡) + 𝑚2𝐼𝑝(𝑡) + 𝑆(𝑡) 𝐼𝑡(0) = 𝐼𝑡𝑏
𝐼��(𝑡) = −(𝑚2 +𝑚4). 𝐼𝑝(𝑡) + 𝑚1. 𝐼𝑡(𝑡) 𝐼𝑝(0) = 𝐼𝑝𝑏
𝐼(𝑡) =𝐼𝑝
𝑉𝑡 𝐼(0) = 𝐼𝑏
(48)
Table 20: Insulin subsystem parameters
Peripheral degradation is known as 𝑚4 (assumed linear)(Man et al., 2007). Refer the hepatic
extraction of insulin (HE)(Man et al., 2007). The insulin flux which leaves the liver is
irreversibly divided by the total insulin flux leaving the liver, the time varies(Man et al., 2007)
Variables Defined
𝐼𝑝 𝑎𝑛𝑑 𝐼𝑙(pmol/kg) Insulin masses in plasma and liver.
𝐼(pmol/kg) Plasma insulin concentration.
𝑏 Denotes basal state.
S(pmol/kg/min) Insulin secretion.
𝑉𝐼(l/kg) Distribution volume of insulin
𝑚1, 𝑚2, 𝑚4 Rate parameters (min-1
)
𝐷 Degradation in both liver and peripheral.
64
65
Table 21: Model parameters of normal and type 2 diabetic patients
The time course HE to that of insulin secretion, 𝑆 as shown below:
𝐻𝐸(𝑡) = −𝑚5. 𝑆(𝑡) + 𝑚6, 𝐻𝐸(0) = 𝐻𝐸𝑏 (49)
Hence,
66
𝑚3(𝑡) =𝐻𝐸(𝑡).𝑚1
1 − 𝐻𝐸(𝑡) (50)
At Basal Steady State,
𝑚6 = 𝑚5. 𝑆𝑏 + 𝐻𝐸𝑏
𝑚3(0) =𝐻𝐸𝑏𝑚1
1 − 𝐻𝐸𝑏
𝑆𝑏 = 𝑚3(0). 𝐼𝑡𝑏 +𝑚4. 𝐼𝑝𝑏 = 𝐷𝑑 (51)
Given that the liver is responsible of 60 % insulin clearance in the steady state has:
𝑚2 = (𝑆𝑏𝐼𝑝𝑏
−𝑚4
1 − 𝐻𝐸𝑏) .1 − 𝐻𝐸𝑏𝐻𝐸𝑏
𝑚4 =2
5.𝑆𝑏𝐼𝑝𝑏
. (1 − 𝐻𝐸𝑏) (52)
Table 22 : Insulin Clearance Parameters
Variables Defined
𝑆𝑏 Basal secretion.
𝐻𝐸𝑏 Basal hepatic secretion fixed 0.6.
𝐼𝑝𝑏 Basal insulin secretion.
𝑚2,4,5,6 Parameters of insulin kinetic
67
Figure 7: The unit process model and identification of glucose-insulin subsystem.
68
Figure 8: Unit Process Models
EGP, the functional description of this term of glucose and insulin signals is explained and
comprises a direct glucose signal and both delayed and anticipated insulin signal(Man et al.,
2007):
𝐸𝐺𝑃(𝑡) = 𝑘𝑝1 − 𝑘𝑝2. 𝐺𝑃(𝑡) − 𝑘𝑝3. 𝐼𝑑(𝑡) − 𝑘𝑝4. 𝐼𝑝𝑜(𝑡)
𝐸𝐺𝑃(0) = 𝐸𝐺𝑃𝑏 (53)
Table 23: EPG parameters
Variables Defined
𝐼𝑝𝑜(pmol/kg) Amount of insulin in portal vein.
𝐼𝑑(pmol/l) Delayed insulin.
Chain of 2 compartments as shown below:
{𝐼1(𝑡) = −𝑘𝑖. [𝐼1(𝑡) − 𝐼(𝑡)] 𝐼1(0) = 𝐼𝑏
𝐼��(𝑡) = −𝑘𝑖. [𝐼𝑑(𝑡) − 𝐼1(𝑡)] 𝐼𝑑(0) = 𝐼𝑏 (54)
Table 24: Two compartments parameters
Variables Defined
𝑘𝑝1(mg/kg/min) Extrapolated EGP at zero glucose and insulin.
69
𝑘𝑝2(min-1
) Liver glucose effectiveness.
𝑘𝑝3(mg/kg/min per
pmol/l)
Parameter governing amplitude of insulin action in liver.
𝑘𝑝4(mg/kg/min per
pmol)
Parameter governing amplitude of portal insulin action in the
liver.
𝑘𝑖(min-1
) Rate parameter accounting for delay between insulin signal and
insulin action.
EGP value is always positive or in other word EGP > 0, at basal steady state:
𝑘𝑝1 = 𝐸𝐺𝑃𝑏 + 𝑘𝑝2. 𝐺𝑃𝑏 + 𝑘𝑝3. 𝐼𝑏 + 𝑘𝑝4. 𝐼𝑝𝑜𝑏 (55)
Glucose rate of appearance is a physiological model of a glucose intestinal absorption
which described the glucose transit through stomach and intestine, assuming the stomach, be to
represent by 2 compartments, one for solid and other triturated phase(Man et al., 2007). A single
compartment is used to describe the following parameters(Man et al., 2007).
𝑄𝑠𝑡𝑜(𝑡) = 𝑄𝑠𝑡𝑜1(𝑡) + 𝑄𝑠𝑡𝑜2(𝑡) 𝑄𝑠𝑡𝑜(0) = 0
��𝑠𝑡𝑜1(𝑡) = −𝑘𝑔𝑟𝑖 . 𝑄𝑠𝑡𝑜1(𝑡) + 𝐷. 𝑑(𝑡) ��𝑠𝑡𝑜1(0) = 0
��𝑠𝑡𝑜2(𝑡) = −𝑘𝑒𝑚𝑝𝑡(𝑄𝑠𝑡𝑜). 𝑄𝑠𝑡𝑜2(𝑡) + 𝑘𝑔𝑟𝑖 . 𝑄𝑠𝑡𝑜(𝑡) 𝑄𝑠𝑡𝑜2(0) = 0
��𝐺𝑢𝑡 = −𝑘𝑎𝑏𝑠. 𝑄𝐺𝑢𝑡(𝑡) + 𝑘𝑒𝑚𝑝𝑡(𝑄𝑠𝑡𝑜). 𝑄𝑠𝑡𝑜2(𝑡) 𝑄𝐺𝑢𝑡(0) = 0
𝑅𝑎(𝑡) =𝑓. 𝑘𝑎𝑏𝑠. 𝑄𝑔𝑢𝑡(𝑡)
𝐵𝑊 𝑅𝑎(0) = 0 (56)
70
Table 25: Single compartment parameters
Variables Defined
𝑄𝑠𝑡𝑜(mg) Amount of glucose in stomach.
𝑄𝑠𝑡𝑜1(mg) Solid phase.
𝑄𝑠𝑡𝑜2(mg) Liquid phase.
𝑄𝐺𝑢𝑡(mg) Glucose mass in intestine.
𝑘𝑔𝑟𝑖(min-1
) Rate of grinding.
𝑘𝑒𝑚𝑝𝑡(min-1
) Rate constant of emptying gastric.
𝑘𝑎𝑏𝑠(min-1
) Rate constant of intestinal absorption.
𝑓 Fraction of intestine absorption appears in plasma.
𝐷(mg) Amount of ingested glucose.
BW(kg) Body weight.
𝑅𝑎(mg/kg/min) Appearance rate of glucose in plasma.
Glucose utilization described by body tissue during the intake of meal. Insulin independent
utilization takes place in first compartment, is constant and represent glucose uptake by the brain
and red blood cells (𝐹𝑐𝑛𝑠)(Man et al., 2007).
𝑈𝑖𝑖(𝑡) = 𝐹𝑐𝑛𝑠 (57)
Insulin dependent utilization takes place in the remote compartment and depends non-
linearly from glucose in the tissue(Man et al., 2007).
𝑈𝑖𝑑(𝑡) =𝑉𝑚(𝑋(𝑡)). 𝐺𝑡(𝑡)
𝐾𝑚(𝑋(𝑡)) + 𝐺𝑡(𝑡) (58)
71
We may define 𝑉𝑚(𝑋(𝑡)) 𝑎𝑛𝑑 𝐾𝑚(𝑋(𝑡)) as linear dependent from remote insulin𝑋(𝑡)
𝑉𝑚(𝑋(𝑡)) = 𝑉𝑚0 + 𝑉𝑚𝑥. 𝑋(𝑡)
𝐾𝑚(𝑋(𝑡)) = 𝐾𝑚0 + 𝐾𝑚𝑥. 𝑋(𝑡) (59)
𝑋(𝑝𝑚𝑜𝑙/𝐿) is the insulin in interstitial fluid may defined as the following equation:
��(𝑡) = −𝑝2𝑈. 𝑋(𝑡) + 𝑝2𝑈[𝐼(𝑡) − 𝐼𝑏] 𝑋(0) = 0 (60)
Table 26: Insulin in interstitial fluid parameters
Variables Defined
𝐼 Plasma insulin.
𝑏 Denotes basal state.
𝑝2𝑈(min-1
) Rate constant of insulin action on the peripheral glucose utilization.
Total glucose utilization U hence may be defined as:
𝑈(𝑡) = 𝑈𝑖𝑖(𝑡) + 𝑈𝑖𝑑(𝑡) (61)
While at basal steady state:
72
𝐺𝑡𝑏 =𝐹𝑐𝑛𝑠 − 𝐸𝐺𝑃𝑏 + 𝑘1. 𝐺𝑝𝑏
𝑘2 (62)
𝑈𝑏 = 𝐸𝐺𝑃𝑏 = 𝐹𝑐𝑛𝑠 +𝑉𝑚0. 𝐺𝑡𝑏𝐾𝑚0 + 𝐺𝑡𝑏
(63)
𝑉𝑚0 =(𝐸𝐺𝑃𝑏 − 𝐹𝑐𝑛𝑠). (𝐾𝑚0 + 𝐺𝑡𝑏)
𝐺𝑡𝑏 (64)
Insulin secretion model used to describe pancreatic insulin secretion, these are the related
equation:
𝑆(𝑡) = 𝛾. 𝐼𝑝𝑜(𝑡) (65)
𝐼��𝑜(𝑡) = −𝛾. 𝐼𝑝𝑜(𝑡) + 𝑆𝑝𝑜(𝑡), 𝐼𝑝𝑜(0) = 𝐼𝑝𝑜𝑏 (66)
𝑆𝑝𝑜(𝑡) = {𝑌(𝑡) + 𝐾. 𝐺(𝑡) + 𝑆𝑏 𝑓𝑜𝑟 �� > 0
𝑌(𝑡) + 𝑆𝑏 𝑓𝑜𝑟 �� ≤ 0 (67)
Table 27: Pancreatic insulin secretion parameters
Variables Defined
𝛾(min-1
) Transfer rate between portal vein and liver.
K(pmol/kg per
mg/dl)
Pancreatic response to the glucose rate of change.
α(min-1
) Delay between glucose signal and insulin secretion.
β(pmol/kg/min per
mg/dl)
Pancreatic response to glucose.
ℎ(mg/dl) Threshold level of glucose above which the β-cells initiate to
73
produce new insulin.
Glucose renal excretion by kidney occurs in plasma glucose exceeds at certain threshold,
hence the linear relationship with plasma glucose as shown below:
𝐸(𝑡) = {𝑘𝑒1. [𝐺𝑝(𝑡) − 𝑘𝑒2] 𝑖𝑓 𝐺𝑝(𝑡) > 𝑘𝑒20 𝑖𝑓 𝐺𝑝(𝑡) ≤ 𝑘𝑒2
(68)
𝑘𝑒1 (min-1
) definition is the glomerular filtration rate and 𝑘𝑒2 (mg/kg) renal threshold of
glucose(Man et al., 2007).
2.8.3.2 MSM Targeted Patient
A total of 204 normal individuals age between 54 and 58 with the mass 77-79 kg receive the
mixed meal containing 1 ± 0.02 g/kg of glucose(Man et al., 2007).
2.8.4 Computer Based Insulin and Manual Protocol
Computer-based insulin infusion protocol is a research has been done regarding this
protocol improves hyper/hypoglycemia control over manual protocol. Computer-based
intravenous insulin therapy protocol integrated within an existing care provider order entry
(CPOE) system improved blood glucose control(Boord et al., 2007). Utility of integrating a
computer insulin therapy decision tool into a CPOE system to improve initiation(Boord et al.,
74
2007) and maintenance of tight glucose control. It is found that computer based insulin infusion
is widely used in surgical intensive care unit (SICU) critically ill patients(Boord et al., 2007).
The patients receiving mechanical ventilation who achieved precise glycemia(Boord et al., 2007)
control (goal 80–110 mg/dl) on an intravenous insulin therapy protocol experienced reduced
rates of in hospital mortality(Boord et al., 2007), bloodstream infection, polyneuropathy, and
renal failure. Computer based protocol improved glycemia control(Boord et al., 2007) in the
SICU population as a whole (all patients ecologic analysis), and if, at the patient level, the
computer-based protocol improved glycemia control(Boord et al., 2007) for patients who
received intravenous insulin therapy continuously for at least 24 hours(Boord et al., 2007). SICU
practice changed so that if a patient’s blood glucose exceeded 110 mg/dl(Boord et al., 2007), a
SICU physician would initiate the CPOE-based SICU insulin protocol,which the patient’s nurse
would carry out(Boord et al., 2007).
The physician initiation screen(Boord et al., 2007) (Fig. 1) requires entry of the current
(initial) blood glucose value, and target high and low glucose limits (default 80–110
mg/dl)(Boord et al., 2007); it includes optional instructions for nurses to notify physicians about
out-of-range values(Boord et al., 2007). At initiation, a highlighted prompt reminds physicians to
provide a dextrose source (intravenous or enteral feedings) to prevent hypoglycemia(Boord et al.,
2007). After verifying protocol parameters, the physician clicks “calculate drip rate”
75
Figure 9: Screenshots of computer intravenous insulin therapy protocol.
The CPOE system generates corresponding orders for physician(Boord et al., 2007)
verification, and instructs the nurse to perform subsequent bedside blood glucose testing every
1–2 hours(Boord et al., 2007) and use the CPOE protocol to maintain glycemia control(Boord et
al., 2007). Nurses enter protocol-mandated glucose readings into the system’s (Boord et al.,
2007)“titration page”as shown in figure 2, and adjust insulin drip rates based on
recommendations provided(Boord et al., 2007). The system logs all entered glucose values,
recommended insulin infusion rates, and any nurse-initiated deviations(Boord et al., 2007),
which become part of the patient’s electronic medical record(Boord et al., 2007).
The formula for insulin dose as shown below :
76
𝐼𝑛𝑠𝑢𝑙𝑖𝑛 𝑑𝑜𝑠𝑒 (𝑢𝑛𝑖𝑡𝑠
ℎ𝑜𝑢𝑟) = (𝑏𝑙𝑜𝑜𝑑 𝑔𝑙𝑢𝑐𝑜𝑠𝑒 𝑖𝑛
𝑚𝑔
𝑑𝑙− 60) 𝑥 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 (69)
Initially 0.03, the multiplier can never fall below zero(Boord et al., 2007). Blood glucoses
exceeding the high target threshold on two consecutive readings, or exceeding 200 mg/dl on one
reading(Boord et al., 2007), trigger a multiplier increase of 0.01(Boord et al., 2007).
Blood glucoses under the low target(Boord et al., 2007) threshold decrease the multiplier
0.01, and glucoses below 60 mg/dl decrease the multiplier by 0.02(Boord et al., 2007). Glucose
readings below target thresholds generate an order for intravenous 50% dextrose dose in 5 ml
increments (based on degree of hypoglycemia)(Boord et al., 2007) to prevent or correct
hypoglycemia simultaneously, intravenous insulin infusion is withheld for one hour(Boord et al.,
2007). The study included consecutive patients more than 18 years of age admitted to the SICU
during the pre- and post-intervention periods(Boord et al., 2007), regardless of whether they
received insulin in the SICU(Boord et al., 2007). For a patient-level analysis, SICU patients been
select to study patients with continuously active intravenous insulin infusion orders for 24 hours
(at some point during their SICU stay), who also had at least four blood glucose measurements
during each 24 hour period (Boord et al., 2007)of insulin infusion(Boord et al., 2007). Only the
first SICU admission per patient qualified for the study(Boord et al., 2007).
77
Table 28 : Percentage of blood glucose readings in range for all patients by SICU
2.9 Critically Ill Patients
Critical care medicine specializes in caring for the most seriously ill patients. These patients
are best treated in an Intensive Care Unit (ICU) staffed by experienced personnel. Some
hospitals maintain separate units for special populations (example, cardiac, surgical, neurologic,
pediatric, or neonatal patients). ICUs have a high nurse is to patient ratio to provide the necessary
high intensity of service, including treatment and monitoring of physiologic parameters and
prevention of infection, stress ulcers and gastritis and pulmonary embolism. Because 15 to 25%
of patients admitted to ICUs die there (Takrouri, 2004 #60), physicians should know how to
minimize suffering and help dying patients maintain dignity.
78
2.9.1 Intensive Unit Care (ICU)
An intensive care unit (ICU), on the other word known as an intensive therapy unit or
intensive treatment unit (ITU) or critical care unit (CCU), is a special department of a hospital or
health care facility that provides intensive care medicine. Intensive care units cater to patients
with severe and life-threatening illnesses and injuries, which require constant, close monitoring
and support from specialist equipment and medications in order to ensure normal bodily
functions{Lemeshow, 1993 #61}. They are staffed by highly trained doctors and nurses who
specialize in caring for critically ill patients. ICU's are also distinguished from normal hospital
wards by a higher staff-to-patient ratio and access to advanced medical resources and equipment
that is not routinely available elsewhere. Common conditions that are treated within ICUs
include Acute Respiratory Distress Syndrome (ARDS), trauma, multiple organ failure and
sepsis{Van den Berghe, 2006 #59}. Patients may be transferred directly to an intensive care unit
from an emergency department if required, or from a ward if they rapidly deteriorate, or
immediately after surgery if the surgery is very invasive and the patient is at high risk of
complications.
79
CHAPTER 3
METHODOLOGY
3.1 Introduction of Statistics
Statistics can be defined as analysis, collection, presentation, organization, and collection of
data. Statistics may be applicable to all types of data including the planning of data collection in
terms of experiments and survey. Statistical analysis has been applied in all fields such as
manufacturing, medical, production planning control and industrial engineering. A sample of
population is required to carry of statistical analysis.
3.1 Selective Statistical Analysis
Case study for this project shows that statistical analysis is the satisfactory method to
outcome with the best result and clear statement of the most suitable protocol and algorithm for
critically ill patients in Malaysia. Out of many analyses, 3 statistical analyses have been chosen
listed below:
1) Mann-Whitney U Test.
2) Regression Analysis (Linear Regression).
3) Analysis Of Variance (ANOVA) Table.
80
3.1.1 Mann-Whitney U Test (MWW U Test)
Mann-Whitney is a test to the independent sample of t-test. It is considered as a non-
parametric test which is used to compare between two population means that come from same
population. This test can also been done on two population to determine their means are equal or
not. Besides, this test is used for equal sample sizes and also used to test the two population
median. Mann-Whitney U test usually used in ordinal data (consist of numerical score).
However, some assumption been made when carrying out Mann-Whitney U Test which has been
listed below:
1) The sample drawn from the population is random
2) Independence within the samples and mutual independence is assumed.
3) Ordinal measurement scale is taken in account.
Mann-Whitney U test is applied in many field, but frequently implemented in
medical/nursing. In medical field is used to know the effect of 2 medicines whether they are
equal or not in terms of curing the ailment.
3.1.1.1 Steps to Carry Out Mann-Whitney U Test.
A sample of 𝑛𝑥 observations {𝑥1, 𝑥2, . . . 𝑥𝑛} in one group and a sample of 𝑛𝑦 observations
{𝑦1, 𝑦2, . . . 𝑦𝑛} in another group.
The Mann-Whitney test is based on a comparison of every observation xi in the first sample
with every observation 𝑦𝑗 in other sample. The total number of pairwise comparison can be made
is 𝑛𝑥 𝑛𝑦 . If the samples have the same median then each 𝑥𝑖 has an equal chance (i.e. probability
1
2 ) of being greater or smaller than each 𝑦𝑗 .
81
Under null hypothesis: 𝐻0 ∶ 𝑃(𝑥𝑖 > 𝑦𝑗) = 1
2 (70)
Under alternative hypothesis 𝐻1 ∶ 𝑃(𝑥𝑖 > 𝑦𝑖) ≠1
2 (71)
The number of times 𝑥𝑖from sample 1 is greater than 𝑦𝑗 from sample 2. This number is
denoted by 𝑈𝑥. Similarly, the number of times 𝑥𝑖 from sample 1 is smaller than 𝑦𝑗 from sample 2
is denoted by𝑈𝑦. Under the null hypothesis we would expect 𝑈𝑥 and 𝑈𝑦 to be approximately
equal.
The observation been arranged in order of magnitude. Under each observation, write down
X or Y (or some other relevant symbol) to indicate which sample they are from.
Under each 𝑥 write down the number of y which are to the left of it (i.e. smaller than it); this
indicates 𝑥𝑖>𝑦𝑗. Under each y write down the number of x which are to the left of it (i.e. smaller
than it); this indicates 𝑦𝑗>𝑥𝑖 .
The total number of times has been adding up 𝑥𝑖 > 𝑦𝑗represent by 𝑈𝑥. The total number of
times has been adding up𝑦𝑗 > 𝑥𝑖 represent by𝑈𝑦. Check that 𝑈𝑥 + 𝑈𝑦 = 𝑛𝑥𝑛𝑦. Calculate
𝑈 = 𝑚𝑖𝑛(𝑈𝑥, 𝑈𝑦)
Statistical table has been used for the Mann-Whitney U test to find the probability of
observing a value of U or lower. If the test is one-sided, this is the p-value; if the test is a two-
sided test, p-value will be obtained by doubling the probability.
82
3.1.1.2 Example of Mann-Whitney U Test
Data below shows the age at diagnosis of type II diabetes in young adults. Does the age at
diagnosis different for males and females?
Males: 19, 22, 16, 29, 24
Females: 20, 11, 17, 12
1. Arrange in order of magnitude:
2. Affix M or F to each observation.
3. Under each M write the number of F to the left of it; under each F write the number of M
to the left of it.
4. 𝑈𝑀 = 2 + 3 + 4 + 4 + 4 = 17, 𝑈𝐹 = 0 + 0 + 1 + 2 = 3
5. 𝑈 = 𝑚𝑖𝑛(𝑈𝑀, 𝑈𝐹 ) = 3
6. Using table for the Mann-Whitney U test we get a two-sided p-value of p = 0.11.
7. Alternate method is also known as normal approximation which can be conducted on large
number of population:
𝑧 =𝑈 −
𝑛𝑥𝑛𝑦
2
√𝑛𝑥𝑛𝑦(𝑁+1)
12
(72)
83
Table 29: Normal approximation parameters
By referring the above example, the variable values are given as,
𝑈 = 3, 𝑛𝑥 = 5, 𝑛𝑦 = 4, 𝑁 = 9, hence the 𝒵 value can be
𝓏 =3 −
(5)(4)
2
√(5)(4)(9+1)
12
𝓏 = −1.751
Variables Define
𝓏 𝒵 value/coefficient
𝑈 Rank sum value (choose minimum)
𝑛𝑥 First population sample size
𝑛𝑦 Second population sample size
𝑁
(𝑛𝑥 + 𝑛𝑦) Total number of sample size
84
Hence, refer the 𝓏 − 𝑡𝑎𝑏𝑙𝑒 to obtain the P-value,
Table 30: Z-table
Since the calculated 𝓏 value is between -1.8 and -1.7, which is-1.751, hence interpolation
can be done, it is found that the P-value is 0.12 with a slight different from Mann-Whitney U
Test. The exact test and the normal approximation give slight different results. Conclusion can be
85
drawn that there is no prove that the age at diagnosis is different for males and females, even
though the results are borderline and the insufficient of statistical significance in this case may
just be due to the very small sample. The actual median age at diagnosis is 14.5 years while for
females and 22 for males, which is quite a substantial difference. In this case it would be
advisable to conduct a larger study.
3.1.2 Regression Analysis (Linear Regression)
Regression analysis is one of the approaches for modeling the relationship between a scalar
dependent variable 𝑦 and one or many explanatory variables or independent variables denotes
as 𝑥. However the term ‘linear’ denotes the case of one explanatory variable called simple linear
regression. Regression is widely applied in association between two variables. It is used to find
relationship between 2 variables. Few assumptions have been taken in account in order to use
simple linear regression method:
1) Different response variables have the same variance in their errors.
2) The mean of the response variable is a linear combination of parameters and the predictor
variables.
3) The predictor value 𝑥 can be treated as fixed values rather than random variables.
4) The errors of the response variables are uncorrelated each other.
3.1.2.1 Linear Regression Equations
The linear regression equation is given as:
𝑦 = 𝑎 + 𝑏𝑥 (73)
86
Table 31: Linear Regression Parameters.
Variables Defined
𝑥 𝑎𝑛𝑑 𝑦 Specified variables
𝑏 The slope of the regression line.
𝑎 The interception point of the regression line and the 𝑦 − 𝑎𝑥𝑖𝑠.
The slope formulae, 𝑏 is given as shown below:
𝑏 =𝑁𝛴𝑋𝑌 − (𝛴𝑋)(𝛴𝑌)
𝑁𝛴𝑋2 − (𝛴𝑋)2 (74)
Table 32: Slope Parameters
The interception formulae, 𝑎 is given as:
𝑎 =𝛴𝑌 − 𝑏(𝛴𝑋)
𝑁 (75)
Variables Defined
𝑁 Number of values or elements.
𝑋 First score.
𝑌 Second Score.
𝛴𝑋𝑌 Sum of the product of first and second score.
𝛴𝑋 Sum of first score.
𝛴𝑌 Sum of second score.
𝛴𝑋2 Sum of square for first score.
87
3.1.2.2 Steps and Example of Simple Linear Regression.
Given the following 𝑋 and 𝑌 values,
Table 33: X and Y values
𝑋 𝑌
60 3.1
61 3.6
62 3.8
63 4.0
65 4.1
1. Identified 𝑁 = 5.
2. Calculate 𝑋𝑌, 𝑋2, 𝛴𝑋, 𝛴𝑌, 𝛴𝑋𝑌, 𝛴𝑋2for the data.
Table 34: Statistic calculation
𝑋 𝑌 𝑋2 𝑋𝑌
60 3.1 3600 186
61 3.6 3721 219.6
62 3.8 3844 235.6
63 4.0 3669 252
65 4.1 4225 266.5
𝛴𝑋 = 311 𝛴𝑌 = 18.6 𝛴𝑋2 = 19359 𝛴𝑋𝑌 = 1159.7
3. Substitute the above values into the slope formula to find 𝑏,
88
𝑏 =5(1159.7) − (311)(18.6)
5(19359) − (311)2
𝑏 = 0.19
4. Substitute the above values into the interception formula to find 𝑎,
𝑎 = 18.6 − (0.19)(311)
5
𝑎 = −8.098
5. Substitute 𝑎 and 𝑏 values into the linear regression equation, hence
𝑦 = −8.098 + 0.19𝑥
Figure 10: Figure shows the linear regression trend line been generated by using Microsoft
Excel
89
3.1.3 One Way Anaysis of Variance (ANOVA)
A One-Way Analysis of Variance is a way to test the equality of three or more means at one
time by using variances. The sums of squares SST and SSE computed for the one-way ANOVA
are used to form two mean squares, one for treatments and the second for error. These mean
squares are denoted by MST and MSE, respectively. These are typically displayed in a tabular
form, known as an ANOVA Table. The ANOVA table also shows the statistics used to test
hypotheses about the population means. When the null hypothesis of equal means is true, the two
mean squares estimate the same quantity (error variance), and should be of approximately equal
magnitude. In other words, their ratio should be close to 1. If the null hypothesis is false, MST
should be larger than MSE. Some assumptions have been made for analysis of variance:
1) The populations from which the samples were obtained must be normally or
approximately normally distributed.
2) The samples must be independent.
3.1.3.1 ANOVA Equations and Table
The mean squares are formed by dividing the sum of squares by the associated degrees of
freedom.
𝑁 = ∑𝑛𝑖 (76)
The degree of freedom for treatment is:
90
𝐷𝐹𝑇 = 𝑘 − 1 (77)
The degree of freedom for error is:
𝐷𝐹𝐸 = 𝑁 − 𝑘 (78)
The corresponding mean square is:
𝑀𝑆𝑇 =𝑆𝑆𝑇
𝐷𝐹𝑇 (79)
𝑀𝑆𝐸 =𝑆𝑆𝐸
𝐷𝐹𝐸 (80)
For 𝐹 − 𝑡𝑒𝑠𝑡, used in testing the equality of treatment means is:
𝐹 =𝑀𝑆𝑇
𝑀𝑆𝐸 (81)
The critical value is the tabular value of the 𝐹 distribution, based on the chosen 𝛼 level and
the degrees of freedom 𝐷𝐹𝑇 and 𝐷𝐹𝐸.
91
Table 35: ANOVA table calculation
Source 𝑆𝑆 𝐷𝐹 𝑀𝑆 𝐹
Treatment 𝑆𝑆𝑇 𝑘 − 1 𝑆𝑆𝑇
(𝑘 − 1)
𝑀𝑆𝑇
𝑀𝑆𝐸
Error 𝑆𝑆𝐸 𝑁 − 1 𝑆𝑆𝐸
(𝑁 − 𝑘)
Total (corrected) 𝑆𝑆𝑇𝑜𝑡𝑎𝑙 𝑁 − 𝑘
The word "source" stands for source of variation. Some authors prefer to use "between" and
"within" instead of "treatments" and "error", respectively.
92
3.1.3.2 Example of ANOVA Table Calculation
The data below resulted from measuring the difference in resistance resulting from
subjecting identical resistors to three different temperatures for a period of 24 hours. The sample
size of each group was 5. In the language of design of experiments, we have an experiment in
which each of three treatments was replicated 5 times.
𝑥1 𝑥12 𝑥2 𝑥2
2 𝑥3 𝑥32
6.9 47.61 8.3 68.89 8.0 64.00
5.4 29.16 6.8 46.24 10.5 110.25
5.8 33.64 7.8 60.84 8.1 65.61
4.6 21.16 9.2 84.64 6.9 47.61
4.0 16.00 6.5 42.25 9.3 86.49
∑𝑥1 = 26.7 ∑𝑥12
= 147.57
∑𝑥2 = 38.6 ∑𝑥22
= 302.86
∑𝑥3 = 42.8 ∑𝑥32
= 373.96
𝑀1 =26.7
5= 5.34
𝑀2 =
38.6
5= 7.72
𝑀3 =
42.8
5= 8.56
𝑆𝑆𝑇𝑜𝑡𝑎𝑙 = (147.57 + 302.86 + 373.96) −(26.7 + 38.6 + 42.8)2
15
𝑆𝑆𝑇𝑜𝑡𝑎𝑙 = 45.3493
𝑆𝑆𝑇 = [(26.7)2
5+(38.6)2
5+(42.8)2
5] −
(26.7 + 38.6 + 42.8)2
15
𝑆𝑆𝑇 = 27.8973
𝑆𝑆𝐸 = 𝑆𝑆𝑇𝑜𝑡𝑎𝑙 − 𝑆𝑆𝑇
𝑆𝑆𝐸 = 45.3493 − 27.8973
𝑆𝑆𝐸 = 17.452
93
Table 36: Value Substitution in ANOVA table
Table 37: F- table
The test statistic is the 𝐹 − 𝑣𝑎𝑙𝑢𝑒 of 9.5913. Using α of 0.05, 𝐹0.05:2,12.Since the test
statistic is much larger than the critical value=3.89, rejecting the null hypothesis of equal
population means and conclusion made has been made that there is a (statistically) significant
difference among the population means. The 𝑝 − 𝑣𝑎𝑙𝑢𝑒 for 9.5913 is 0.00325, so the test
statistic is significant at that level.
Source 𝑆𝑆 𝐷𝐹 𝑀𝑆 𝐹
Treatment 27.8973 2 13.9487 9.5913
Error 17.452 12 1.4543
Total (corrected) 45.3493 14
94
3.2 Flow Chart
Figure 11 : Flow Chart
No
95
CHAPTER 4
RESULT
Collaboration has been done with Tengku Ampuan Afzan Hospital (HTAA) and
Christchurch Hospital together 91 and 349 ICU patient’s data obtained from HTAA and
Christchurch respectively. These ICU patient’s blood glucose has been monitored every hour in a
week, together the particular concentration of insulin been infused on every patients for specified
hour in a week. It has been found that HTAA and Christchurch practicing respective blood
glucose protocol known as Hospital Tengku Ampuan Afzan (HTAA) protocol and Specialized
Relative Insulin and Nutrition Tables (SPRINT) protocol. The aim of this chapter is to find out
whether both protocols are similar in their goal or totally different from the goal. Besides to find
out the data obtained from both hospitals are significant or not. Therefore, statistical analysis
method has been chosen to solidify and outcome with the statement by using Microsoft Excel.
The patient’s code in HTAA recognize as ‘GXXX’ while for Christchurch hospital is ‘5XXX’
where ‘X’ represent the number.
4.2 Scatter Plot
The patient’s data from both hospitals were transferred into Microsoft Excel, the average of
blood glucose concentration and insulin infusion concentration for each patient were calculated
in Microsoft Excel for 91 patients from HTAA followed by 394 patients from Christchurch. Two
graphs have been generated for each hospital patient’s data using Microsoft Excel in the form of
scatter plot under 95% confidence interval. One is average blood glucose upon patients another
96
is insulin infusion upon patients. The exact values of 1st quartile and 3
rd quartile under 95%
confidence interval are not identify since form the plot it is not possible unless of estimation,
later the data been generated in ‘Descriptive Statistic’ together will obtain the grand mean, mode
and median as well using Analysis Tool pack in Microsoft Excel. Based on the scatter plot, this
subtopic is to identify the outliers patients and extract their information besides finding the
reasoning of been in such way.
97
4.2.1 Scatter Plot of Average Blood Glucose for HTAA and SPRINT
Protocols.
Figure 12: Average Blood Glucose upon Patients for HTAA
Based on Figure 11, most of the average blood glucose data are within the interval of 97.5%
(3rd
quartile) and 2.5% (1st quartile) for 95% confidence interval. Out of 91 patients, it is found
that 90 patient’s average blood glucose data are within the line intervals. Only one patient’s data
is out of the range and known as an outlier since the data is beyond 97.5% line. Most of the ICU
patients might adapt to HTAA protocols based on the scatter plot. Since all 91 patients are from
different ages, gender, weight, height and ethnicity (Malay, Chinese, Indian and Foreigner)
according to the patients demographic (In Appendix), there is a chance that their average blood
glucose been control by HTAA protocol by suitable amount of insulin infusion.
98
Table 38: Blood Glucose Analysis for HTAA protocol
Based on table 37, the grand mean for the blood glucose is 8.71 U/hour while the median
and mode are 8.39 U/hour and 8.26 U/hour respectively. The 1st quartile and 3
rd quartile for 95 %
confidence interval are 7.12 U/hour and 15.36 U/hr. In terms of measuring the central tendency,
this data is in such way mode < median < mean. Hence, the values for 95 % confidence interval
are 8.39 U/hour [7.12 U/hour, 15.36 U/hour]. The patient’s data which is consider as outlier is
extracted from the patients demographic and tabulated for average blood glucose of HTAA
protocol as shown below.
Table 39: Outlier Data
Patient
Code
Age Gender Ethnicity Height(cm) Weight(kg) BMI Diagnosis Death Dialysis
G065 26 Male Malay 160 75 29.3 Leptospirosis No No
99
Based on table 39, the patient, G065 suffers from Leptospirosis, is a kind of an infectious
bacterial disease transmitted through blood (Bharti, 2003). There is a chance that this patient is
facing a blood related illness and needed to be given a high federate, causing to have an extreme
average blood glucose level as shown in Figure 11, which is 15.7 U/hour, in addition based on
the body mass index, this patient is overweight which is 29.3 considering another factor of
having high average blood glucose.
100
Figure 13: Average Blood Glucose upon Patients for Christchurch
Based on figure 12, most of the average blood glucose data are within the interval of 97.5%
(3rd
quartile) and 2.5% (1st quartile) for 95% confidence interval. Out of 394 patients, it is found
that 392 patient’s average blood glucose data are within the line intervals. There are 2 patients
data are out of range where one is beyond 97.5 % line while another is below 2.5% line. Since all
394 patients are from different ages, gender, weight, height according to the patients
demographic (In Appendix), there is a chance that their average blood glucose been control by
SPRINT protocol by suitable amount of insulin infusion.
More outliers been found in Figure 12 compared to that of Figure 11. But, the data
significant level is still undefined, with only scatter plot doesn’t shown any strong evidence of
how significant it is. Therefore, some statistical analysis been carried out to valid the statement.
101
Table 40: Blood Glucose Analysis for SPRINT Protocol
Based on table 38, the grand mean for the blood glucose is 6.34 U/hour while the median
and mode are 6.53 U/hour and 6.03 U/hour respectively. The 1st quartile and 3
rd quartile for 95 %
confidence interval are 4.49 U/hour and 16.05 U/hour. In terms of measuring the central
tendency, this data is in such way mode < mean < median. Hence, the values for 95 %
confidence interval are 6.53 U/hour [4.49 U/hour, 16.05 U/hour]. The patient’s data which are
consider as outlier are extracted from the patients demographic and tabulated for average blood
glucose of SPRINT protocol as shown below.
102
Table 41: Outlier Data
Patient
Code
Age Gender Diagnosis
Code
5087 72 Male CAH,
COL
5113 55 Female RPLA,
SGLBO
Unlike HTAA ICU patients, Christchurch patients are diagnosis with more than 1 disease,
the diagnose code obtained from patients demographic and been created in chart form
(Appendix) to make it easier to identify patients diagnosis. All the necessary diagnosis codes
have been described in table form (Appendix). Based on table 41, it has been found patient 5087
is male with an age of 72 considered as twilight age, suffer from Hypotension, abnormal low
blood pressure and stayed out of hospital. The average blood glucose obtained from the
demographic is 16.2 U/hour. Probably, because of imbalanced diet or blood related problems,
the average blood glucose might be high. Patient 5113 is a female with an age of 55, suffers from
obstruction and aspiration, due to blockage(Hogg, 2004), this patient maybe having breathing
difficulties that led to oxygen demand as well as glucose demand to carry out a proper respiration
process (Altman, 1971). The average blood glucose of patient 5113 is 4.4 U/hour from the
demographic.
.
103
4.2.2 Scatter Plot of Average Insulin Infusion for HTAA and SPRINT
Protocols
Figure 14: Average Insulin Infusion upon Patients for HTAA
Based on figure 13, most of the average insulin infusion data are within the interval of
97.5% (3rd
quartile) and 2.5% (1st quartile) for 95% confidence interval. Out of 91 patients, it is
found that 87 patient’s average insulin infusion data are within the line intervals. There are 3
patients data are out of range where 1 is beyond 97.5 % line while the rest are below 2.5% line.
There might be a chance that the average insulin infusion amount suits based on the average
blood glucose of patients.
104
Table 42 : Insulin Infusion Analysis for HTAA protocol
Based on table 39, the grand mean for the insulin infusion is 2.59 U/hour while the median
and mode are 2.36 U/hour and 2.26 U/hour respectively. The 1st quartile and 3
rd quartile for 95 %
confidence interval are 1.19 U/hour and 5.80 U/hour. In terms of measuring the central tendency,
this data is in such way mode < median < mean. Hence, the values for 95 % confidence interval
are 2.26 U/hour [1.19 U/hour, 5.8 U/hour]. The patient’s data which are consider as outlier are
extracted from the patients demographic and tabulated for average insulin infusion of HTAA
protocol as shown below.
105
Table 43 : Outlier Data
Patient
Code
Age Gender Ethnicity Height(cm) Weight(kg) BMI Diagnosis Death Dialysis
G001 77 Male Malay 170 70 24.2 Pneumonia Yes No
G043 62 Male Malay 150 50 22.2 Leptospirosis No Yes
G051 18 Female Malay 162 80 30.5 Allergy No No
Based on table 42, patient G001 suffers from pneumonia, which is an inflammatory
condition of the lung affecting primarily the microscopic air sacs known as alveoli (Macfarlane,
1982). Probably of breathing difficulties and considering twilight age, there could be possibilities
of organ malfunction may lead to high insulin demand instead of 1 U/hour. However, the
patient’s BMI considered as normal but already faced mortality. Patient G043 suffers from
Leptospirosis same as patient G065, as it is a blood related disease (Bharti, 2003). However this
patient’s BMI consider as healthy, since this patient undergoes dialysis, there is a probability of
high insulin demand considering the twilight age and kidney malfunctions issue (Wolfe, 1999).
Patient G051 at the age of 18 suffers from allergic but now mention specifically in patients
demographic, but her BMI is 30.5 indicates that she is obese. Due to obese there is an imbalance
in average insulin infusion due to imbalance of blood glucose caused by unhealthy diet.
106
Figure 15: Average Insulin Infusion upon Patients for Christchurch
Based on figure 14, most of the average insulin infusion data are within the interval of
97.5% (3rd
quartile) and 2.5% (1st quartile) for 95% confidence interval. Out of 394 patients, it is
found that 391 patient’s average insulin infusion data are within the line intervals. There are 3
patients data are out of range where 2 are beyond 97.5 % line while 1 is below 2.5% line.
Equal number of outliers been found in Figure 14 compared to that of figure 13. But, the
data significant level is still undefined, with only scatter plot doesn’t shown any strong evidence
of how significant it is. Therefore, some statistical analysis been carried out to valid the
statement.
107
Table 44 : Insulin Infusion for SPRINT protocol
Based on table 40, the grand mean for the insulin infusion is 2.9 U/hour while the median
and mode are 2.65 U/hour and 2.00 U/hour respectively. The 1st quartile and 3
rd quartile for 95 %
confidence interval are 0.55 U/hour and 10.33 U/hour. In terms of measuring the central
tendency, this data is in such way mode < median < mean. Hence, the values for 95 %
confidence interval are 2.65 U/hour [0.55 U/hour, 10.33 U/hour]. The patient’s data which are
consider as outlier are extracted from the patients demographic and tabulated for average insulin
infusion of SPRINT protocol as shown below.
108
Table 45 : Outlier Data
Patient
Code
Age Gender Diagnosis
Code
5270 48 Female RPR
5291 59 Male TBF,TA
5388 75 Male GCC
Based on table 45, patient 5270 is a female with an age of 48 suffers from restrictive lung
disease, disorder of lungs parenchyma where the normal lungs tissue become scar (Saxena,
2015). This could be due to breathing difficulties or less glucose level in the body caused to have
an excessive insulin infusion. Patient 5291 is a male with an age of 59, suffers from abdomen
problem together with trauma related to femur (bone/skeleton). Patient 5388 is a male with the
age of 75 suffers from gastrointestinal colon. This patient may have food digestion problems
(Miettinen, 2000) which cause high insulin demand.
109
4.3 Histogram
A histogram is a bar graph that shows the number of times data occur within certain ranges
or intervals. In order to create the histogram in Microsoft Excel, all the data has been arranged in
an interval grouped data. For all the group data, the class width/size has been set to 1 since there
is no huge different between those values in the set of data.
4.3.1 Average Blood Glucose Histogram
Table 46: Group Data of Average Blood Glucose for HTAA Protocol
110
Figure 16 : Histogram of Average Blood Glucose for HTAA Protocol
Based on figure 15, the modal class for the data is 7.5-8.5 U/hour, the mode and median are
lies within the modal class interval which are 8.26 U/hour and 8.49 U/ hour, however the mean is
8.71 U/hour which is not lies between the modal class. The shape distribution is positively
skewed.
111
Table 47 : Group Data of Average Blood Glucose for SPRINT Protocol
Figure 17 : Histogram of Average Blood Glucose for SPRINT Protocol
112
Based on figure 16, the modal class for the data is 5-6 U/hour, the mode, mean and median
are lies within the modal class interval which are 6.03 U/hour, 6.34 U/hour, 6.53 U/hour. The
shape distribution is positively skewed.
4.3.2 Average Insulin Infusion Histogram
Table 48: Group Data of Average Insulin Infusion for HTAA Protocol
113
Figure 18 : Histogram of Average Insulin Infusion for HTAA Protocol
Based on figure 17, the modal class for the data is 1.5-2.5 U/hour, the mode and median are
lies within the modal class interval which are 2.26 U/hour and 2.36U/hour. The mean is 2.59
U/hour which is not lies between the modal class. The shape distribution is positively skewed.
114
Table 49 : Group Data of Average Insulin Infusion for SPRINT Protocol
Figure 19 Histogram of Average Insulin Infusion for SPRINT
115
Based on figure 18, the modal class for the data is 2-3 U/hour, the mode, mean and median
are lies within the modal class interval which are 2.0 U/hour, 2.90 U/hour and 2.65 U/hour. The
shape distribution is positively skewed.
4.4 Linear Regression Analysis
Linear regression analysis is used to compare between two variables ‘X’ and ‘Y’. In order
to find out how close the data is fitted to the regression, finding R squared value also knows as
coefficient of determination is necessary. Generally, R squared value indicates the proportion of
the variance in the dependent variable, Y that is predictable from the independent variable, X
(Seber, 2012). The variables been compared in such way between the average blood glucose of
patients for both hospitals and insulin infusion of patients as well for both hospitals, since the
number of samples for variable X and Y must be equal (Seber, 2012), the number of patients
from Christchurch involve in this analysis are only 91 out of 394 making equal to the number of
patients in HTAA. Theoretical study shows that R squared value greater than 0.5 or 50% brings
the meaning of variables X and Y have a greater correlation and dependent each other (Seber,
2012). In the end of the subtopic, the R square value is required to solidify the statement
assumed for the goal of both protocols. The assumption has been made in such way:
𝑅2 > 0.5, 𝐵𝑜𝑡ℎ 𝐻𝑇𝐴𝐴 𝑎𝑛𝑑 𝑆𝑃𝑅𝐼𝑁𝑇 𝑝𝑟𝑜𝑡𝑜𝑐𝑜𝑙𝑠 𝑚𝑖𝑔ℎ𝑡 𝑏𝑒 𝑠𝑖𝑚𝑖𝑙𝑖𝑎𝑟 𝑖𝑛 𝑡ℎ𝑒𝑖𝑟 𝑔𝑜𝑎𝑙
𝑅2 < 0.5, 𝐵𝑜𝑡ℎ 𝐻𝑇𝐴𝐴 𝑎𝑛𝑑 𝑆𝑃𝑅𝐼𝑁𝑇 𝑝𝑟𝑜𝑡𝑜𝑐𝑜𝑙𝑠 𝑚𝑖𝑔ℎ𝑡 𝑛𝑜𝑡 𝑏𝑒 𝑠𝑖𝑚𝑖𝑙𝑖𝑎𝑟 𝑖𝑛 𝑡ℎ𝑒𝑖𝑟 𝑔𝑜𝑎𝑙
116
4.4.1 Linear Regression of Average Blood Glucose Data for HTAA and
Christchurch
Figure 20 : Regression Graph of Average Blood Glucose Data for HTAA and Christchurch
Based on figure 19, the blue line represents the plot for average blood glucose of patients
upon axis X: Christchurch and Y: HTAA. The red line is the best fit linear line for the plotted
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Ave
rage
Blo
od
Glu
cose
Of
Pat
ien
ts f
rom
Ho
spit
al T
en
gku
Am
pu
an A
fzan
(H
TAA
),U
/hr
Average Blood Glucose Of Patients from Christchurch,U/hr
Plot
Best Fit Line
117
data. It has been found that the red line passes most of the plotted data showing that gradient of
the linear line very significant together with the data.
Table 50 : Summary Output of Average Blood Glucose for HTAA and Christchurch
Regression Statistics
Multiple R 0.71529
R Square 0.51164
Adjusted R Square 0.50615
Standard Error 0.98966
Observations 91
Based on table 46, for 91 (observations) patients from both HTAA and Christchurch
hospitals throughout the regression analysis done by using Microsoft Excel, the R square value
obtained is 0.51164 or 51.16% while the standard error is 0.98966. The R squared value obtained
is greater than the assumed value which is 0.5. Therefore, there is a probability that both
protocols might be same in their goal, since there is a strong correlation between those two
variables (X: SPRINT, Y: HTAA) protocols about 51.16% showing that the regression line fit
the data. However, to valid the statement, another regression analysis has been done for average
insulin infusion of patients.
118
4.4.2 Linear Regression of Average Insulin Infusion Data for HTAA and
Christchurch
Figure 21 : Regression Graph of Average Insulin Infusion Data for HTAA and
Christchurch
Based on figure 20, the blue line represents the plot for average insulin infusion of patients
upon axis X: Christchurch and Y: HTAA. The red line is the best fit linear line for the plotted
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.0 0.5 1.0 1.5 2.0 2.5
Ave
rage
In
sulin
Infu
sio
n o
f P
atie
nts
fo
r H
osp
ital
Tre
ngk
u A
mp
uan
Afz
an,U
/hr
Average Insulin Infusion of Patients for Christchurch,U/hr
Plot
Best Fit Line
119
data. It has been found that the red line passes least of the plotted data showing that gradient of
the linear line less significant together with the data.
Table 51 : Summary Output of Average Blood Glucose for HTAA and Christchurch
Regression Statistics
Multiple R 0.88041
R Square 0.77512
Adjusted R Square 0.77260
Standard Error 0.45044
Observations 91
Based on table 47, for 91 (observations) patients from both HTAA and Christchurch
hospitals throughout the regression analysis done by using Microsoft Excel, the R square value
obtained is 0.77512 while the standard error is 0.45044. The R squared value obtained is greater
the assumed value which is 0.5. A strong correlation of 77.51 % between the two variables (X:
SPRINT, Y: HTAA) protocols can be defined both of them are depend each other in addition of
line fitting the data.
Therefore, 𝑅2 > 0.5, 𝑏𝑜𝑡ℎ 𝐻𝑇𝐴𝐴 𝑎𝑛𝑑 𝑆𝑃𝑅𝐼𝑁𝑇 𝑝𝑟𝑜𝑡𝑜𝑐𝑜𝑙𝑠 𝑚𝑖𝑔ℎ𝑡 𝑏𝑒 𝑠𝑎𝑚𝑒 𝑖𝑛 𝑡ℎ𝑒𝑖𝑟 𝑔𝑜𝑎𝑙
is a valid statement.
120
4.5 One Way Analysis of Variance (ANOVA) Table
ANOVA table has been applied in this project assuming the mode ≈median≈mean since
there is no huge difference in these values because been locate in the modal class, hence all the
histogram shapes assume to be normally distributed. This table been used to find the 𝑝-values in
order to determine whether the data is significant or not, but generally 𝑝-value is used to observe
result to a relative statistical model on how extreme the observation is. In addition, 𝑝-value is
defined as the probability of obtaining a result equal to or "more extreme" than what was actually
observed, assuming that the model is true (Goodman, 1999). In this subtopic, the ANOVA table
been generated under 95% confidence interval in Microsoft Excel, hypothesis statement has been
made in such way:
𝑝 > 0.05, 𝑇ℎ𝑒 𝑑𝑎𝑡𝑎 𝑖𝑠 𝑛𝑜𝑡 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡
𝑝 < 0.05, 𝑇ℎ𝑒 𝑑𝑎𝑡𝑎 𝑖𝑠 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡
4.5.1 ANOVA Table for Average Blood Glucose
Table 52 : ANOVA Analysis for Average Blood Glucose
Source of Variation SS df MS F P-value F critical
Between Groups 413.4228 1 413.4228 201.3941 1.8622E-38 3.8608
Within Groups 991.5050 483 2.0528
Total 1404.9278 484
121
Based on table 48, the 𝑝-value for the average blood glucose obtained is 1.8622E-38 which
is less than 0.05. Hence, 𝑝 < 0.05, 𝑡ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑏𝑙𝑜𝑜𝑑 𝑔𝑙𝑢𝑐𝑜𝑠𝑒 𝑑𝑎𝑡𝑎 𝑖𝑠 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 , this
statement is valid and acceptable. Might be the average blood glucose of patients are adapted to
respective implemented protocols.
4.5.2 ANOVA Table for Average Insulin Infusion
Table 53 : ANOVA Analysis for Average Blood Glucose
Based on table 49, the 𝑝-value for the average insulin infusion obtained is 0.05415 which is
greater than 0.05. Hence, 𝑝 > 0.05, 𝑡ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑠𝑢𝑙𝑖𝑛 𝑖𝑛𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑎𝑡𝑎 𝑖𝑠 𝒏𝒐𝒕 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 ,
this statement is valid and acceptable. Might be the insulin infusion is imbalance due to patient’s
health condition or illness related to blood.
Source of Variation SS df MS F P-value F critical
Between Groups 6.8947 1 6.8947 3.7261 0.05415 3.8608
Within Groups 893.7303 483 1.8504
Total 900.6250 484
122
CHAPTER 5
CONCLUSION
5.1 Introduction
Based on the result obtained in terms the scatter plot, all 4 data looks significant and most
of the plots are within 95% confidence interval line of 1st and 3
rd quartile, only few outliers can
be found in each data. The outlier patient’s data have been extracted and analyzed according to
Body Mass Index (BMI), age, gender, and diagnosis for behaving in such way. When it comes to
the central tendency measurement, all data are in such way 𝑚𝑜𝑑𝑒 < 𝑚𝑒𝑑𝑖𝑎𝑛 < 𝑚𝑒𝑎𝑛 and
the positively skewed shape has been proven by generating the histograms. It has been found the
mode, mean, and median are lies within the modal class. In order to carry out ANOVA table, an
assumption been made in a way 𝑚𝑜𝑑𝑒 ≈ 𝑚𝑒𝑑𝑖𝑎𝑛 ≈ 𝑚𝑒𝑎𝑛 since all the value approaches the
modal class, hence later all the histograms shape is assumed to be normally distributed.
Regression analysis has been done on average blood glucose and average insulin infusion in
order obtained the R-squared value, it has been found that both R-squared values obtained are
greater than 0.5 proving the statement of HTAA and SPRINT protocols are same in their goal
and function. In ANOVA table, the P-value obtained from average blood glucose is less than
0.05 showing the data is significant, on the other hand for average insulin infusion is greater than
0.05 means the data is not significant. By comparing the patients from Christchurch Hospital,
New Zealand and Tengku Ampuan Afzan, Malaysia (HTAA), it is very obvious the insulin
infusion data could be less significant due to environmental factor, ethnicity, height, weight, and
lifestyle.
123
5.2 Recommendation
Since both protocols are same in their goal, it is possible for these hospitals to exchange their
protocols by term of collaboration as there is a strong evidence of both of them are same in
achieving the goal . It has been found both HTAA and Christchurch hospital achieve the target in
a proper way. However, both protocols are not capable to prevent the mortality rate but can
reduce it as proven in previous case study. Therefore, by taking in account the environmental
factor, ethnicity, height, weight, and lifestyle, Both SPRINT and HTAA protocols are suitable
for Malaysian critically ill patients and can be widely implement in all Malaysia’s hospital.
124
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APPENDICES
Gantt chart
Process/Week
1 2 3 4 5 6 7 8 9 10 11 12 13 14 Literature Review Data Collection and Mining Midterm Presentation Statistical Analysis Result Analysis Report Writing Final Presentation
128
Patients Demographic Chart
Hospital Tengku Ampuan Afzan (HTAA), Malaysia
Note: Some data are filter or combined together due similar diagnosis
129
Christchurch Hospital, New Zealand
Note: Some data are filter or combined together due similar diagnosis
130
Relative ICU Diagnosis Code (Christchurch Hospital)
Code Description
CA Cardiac arrest
CAI In hospital
CDB Bradycardia/Asystole
CDVT Ventricular tachycardia
CFS Cardiogenic shock
CII Infarction
COIE Endocarditis
COL Hypotension
COP Pulmonary embolus
COT Effusion/Tamponade
COVAAS Stent
COVATD Thoracic dissection
EMGDK Ketotic
GBI Ischaemia/infarction
GBPC Colon
GHD Duodenal
GIP Peritonitis
GIPB Biliary
GLFE Hepatic encephalopathy
EMGL Hypoglycaemia
131
CAH Out Of Hospital
CFL Left ventricular failure.
SGLBO Obstruction
RPR Restrictive Lung Disease
TBF Trauma related femur (bone)
Source : Christchurch Intensive Care Unit
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133
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