MEASUREMENTS COLE MODEL ANALYSIS F EBIS NEONATAL CEREBRAL

(1)

COLE MODEL ANALYSIS ^O F EBIS NEONATAL CEREBRAL

MEASUREMENTS

PRATHAMESH SHARAD DHANPALWAR

&

XINYUAN CHEN

MASTER DEGREE THESIS 15 ECTS, 2009-10 SWEDEN

(2)

Cole Model Analysis of EBIs Neonatal Cerebral Measurements

Prathamesh Sharad Dhanpalwar Xinyuan Chen

Master thesis

Subject Category: Medical Technology, Signal Processing

University College of Borås School of Engineering SE- 501 90 BORÅS

Telephone +46 033 435 4640

pratham_maverick@yahoo.co.in^; Xinyi86-85@hotmail.com

Examiner: Fernando Seoane Martínez Supervisor: Fernando Seoane Martínez

Date: 27th September 2010

Keywords: Electrical Bioimpedance Spectroscopy, Cole Model, Hook Effect, Signal Analysis, neonates.

(3)

Dedicated

To Parents

&

Everyone Who Have Made This Possible

(4)

ABSTRACT

The concept of Electrical Bio Impedance prevails in this thesis. The EBI measurement which is used for obtaining the body composition is, by virtue of time becoming of great use as its one of the easiest method of finding out the body composition. In simple words, EBI is the opposition offered by the body to the current. It is just like another analysis tool. The result is only as good as the test is done.

In this thesis, we have done the analysis on the neonatal EBI measurements of two kinds.

In this work, 293 measurements are obtained from 12 babies and 230 measurements are obtained from 7 babies have been analyzed with the purpose of obtaining reference values for the spectrum of complex EBI. The analysis uses both statistical and model approach of obtaining reference values and in order to fit the given data, Cole model analysis is used.

Filters were applied to get the highest degree of correctness. In the due course of the filtering, it was found that the measurements from some babies have been deleted. The Standard Error of Estimation (S.E.E.) is a parameter used for obtaining the further reliable and most probable output.

The further analysis is done using MATLAB and the results are been compared to the previous analysis report.

(5)

ACKNOWLEDGEMENT

Thanks to Almighty.

The existence of this thesis work would not be possible without the constant support, great effort and unmatchable gesture and encouragement from our supervisor Prof. Fernando Seoane Martinez. We deeply appreciate the assistance and help he provided in accomplishing this thesis. In the due course of this work, we learnt a lot from him and which is priceless.

We are very grateful to our parents, siblings and family members who were always there by our side and prayed for our welfare.

We would also like to thank our colleagues and friends who always made things easier and simpler for us and made us happy.

Prathamesh Sharad Dhanpalwar & Xinyuan Chen

29

^th

October, Borås

(6)

Chapter 1 INTRODUCTION

1.1 Introduction

Bioelectrical Impedance analysis (BIA) is a common method used to assess the tissue and body composition and analyzing them. It is a wide spread and widely accepted technology used for different applications like medical diagnosis, research, patient monitoring and treatment. This method has become popular because of its simplicity and portability. Among the different methods available for EBI spectroscopy, Cole model offers the possibility to represent and experimental measurement with only four parameters. This project focuses on the spectrum of complex EBI of the neonatal brain.

1.2 Motivation

In the past years, research on EBI spectroscopy has been made on neonatal brain in animals and concluded that it changes with hypoxia. This brings out the need to investigate if the EBI changes in asphyxiated brains in humans neonates which in turn opens the doors for development in new tools screening and monitoring neonates suffering from neonatal asphyxia.

1.3 Goal

The main goal of this project throws light on obtaining the spectral reference values of EBI and Cole parameters from a set of EBI spectroscopy measurements from both healthy and sick neonates.

The secondary goal is also to present a novel way of performing the analysis of EBI values between healthy and sick neonates and correlate them. In this thesis, much work is done on obtaining the reference values which indicate the neonates to the best.

1.4 Work done

EBI spectroscopy data from sick neonates has been analyzed and characterized. The EBI characterization has been done based in the Cole parameters using the Bioimp software MS Excel and MATLAB. Both groups of data have been characterized and the S.E.E of the produced curve fitting is taken to be the quantitative measure of correctness. The set of Cole parameters obtained from classes have been analyzed to look for possible classification features.

(9)

1.5 Structure

The whole thesis report is organized in six chapters and the references. Chapter 1 is the introduction part of the thesis work. Chapter 2 gives a brief background of the electrical properties of the tissues, Cole model, EBI measurements and the bases about how EBI technology can detect tissue injury. Chapter 3 discussed briefly the sector of the population and how the measurements were taken, as well as the equipment used. Furthermore, it describes the method used to realize the study. Chapter 4 contains the results obtained during the analysis. Chapter 5 discusses the final results obtained from the analysis. The last Chapter contains the conclusion and proposed future work.

(10)

Chapter 2 ELECTRICAL BIOIMPEDANCE

2.1 Introduction

Electrical bioimpedance (EBI) is commonly measured for estimating body and tissue composition. Though the electrical properties of the tissue were discussed from the late 18^th century, the study and advancement in EBI were made in 1970s. The analysis is very straight forward. The better the tests are carried out, the better are the results though some care has to be taken while doing the experiments and tests. The opposition offered by the body tissues to the fluids flowing inside the body is called body impedance. Analysis indicates that measurements of body impedance can be used to acquire fluid volumes, for example, total body water (TBW) in the neonate [1].

2.2 Electrical properties of tissues

The electrical properties of tissue and the cell suspension have been used for a wide range of biomedical applications. Much research work has been done until now and is still undergoing to find out the applications of EBI in various fields. Diagnosis and treatment of various physiological conditions with weak electric currents, radio-frequency hyperthermia, electrocardiography, and body composition are some of the application worked and practiced on till now [2]. The electrical conductance of the biological tissue depends on its constituents. Many cells together constitute a tissue and each cell has a lipid bi-layer plasma membrane with protoplasm comprising of cytosol, organelles and the nucleus of the cell.

The cell conducts the electric current as the ions in it act as charge carrier and the tissue fluid along with cell fluid act as electrolyte where the free movement of charge takes place-giving rise to electric current. This is as same as that of electrons in metals.

Figure 2.1: The composition of cell

(11)

Table 2.1: Typical ion concentrations in mammalian cytosol and blood

Ion Concentration in cytosol (millimolar)

Concentration in blood (millimolar)

Potassium 139 4

Sodium 12 145

Chloride 4 116

Bicarbonate 12 29

Amino acids &

proteins 138 9

Magnesium 0.8 1.5

Calcium <0.0002 1.8

(Data obtained from [3])

Every living organism also has dielectric properties at every level (cellular, molecular, tissue).

This is produced by polar elements that can orient their electrical pole in the direction of a gradient field and therefore the dielectric properties are contributed by cell constituents and cell organelles.

Thereby, this dielectric medium with lipid bilayer act as a capacitor with an approximate capacitance of 0.01 F/m2 [4].

The dielectric properties also depend upon the composition of cells, its organelles, structure of tissue, etc. Therefore, by the above-mentioned properties, a cell can be assumed to be as similar to a simple electrical circuit with a capacitor and with its conductance.

Figure 2.2: Bi-lipid layer in cell membrane

(12)

2.3 Electrical equivalent of cell

In reality, most materials including biological tissues act as both dielectric conductor as it has immobile charges that can be polarized but they do not move and free charges that contribute to the current flow.

The electrical properties of tissue are given by the cell and tissue constituents and their structure.

An equivalent model of cell is represented in the below figure 2.3.

2.4 Frequency dependent EBI

For living tissues, both the permittivity and the conductivity are depending on frequency. This dependence is named dispersion. The dispersion can be sorted into four major classes, α-dispersion, β-dispersion, γ-dispersion, and δ-dispersion. At the frequency range of the Beta dispersion, the Cole model equation was found. Four parameters are applied in this equation and it can plot the Cole plot.

2.4.1 Cole equation

The EBI measurement of any biological tissue is given by the Cole equation

(2.1) Where

R₀ = Resistance at DC frequency R∞ = Resistance infinite frequency

τ = Time constant (RC) and α = 1 in a typical RC circuit (Cole, 1940)

2.4.2 Dispersion in tissue

According to Grimnes and Martinsen, for all the biomaterials, the dispersion is evident as a function of frequency under electrical examinations, which is also evident from the above mentioned

Figure 2.3: Electrical Equivalent of cell. The circuit (a) is the one relying on cell membrane and the intra- and extra- environment of it. The circuit (b) is the equivalent of circuit (a) and the circuit (c) is the simplification of the circuit (b)

(13)

Cole equation as the equation has which is equivalent to . Thereby, the dispersion here occurs as a function of frequency [5]. The dispersions are classified into four types and they are α-dispersion, β-dispersion, γ-dispersion, and δ –dispersion. More information can be found on this in (Grimnes &

Martinssen 2008) 2nd edition.

Table 2.2: Dielectric dispersions (Grimnes & Martinsen, 2008 2nd edition) Type Frequency

range

Main Mechanism

α mHz-kHz Counter ion effects near the membrane surfaces, active cell membrane effects and gate channels, intracellular structures and ionic diffusion, dielectric losses.

β 0.01 – 100 MHz Maxwell- Wagner affects, passive cell membrane capacitance, intra cellular organelle membranes, protein molecule response.

γ 0.1 – 100 GHz Dipolar mechanisms in polar media such as water, salts and proteins.

2.5 EBI measurements

From the mid 90’s, the measurement of EBI has been playing a crucial role in the medical field.

In order to know the correct EBI measurements or in other words to do the correct EBI analysis, one must know the details of the specific conductivities and relative permittivity of biological tissue. The table below can give a further more insight on this.

Figure 2.4: Dielectric dispersions (permittivity on the left and conductivity on the right) in the brain grey matter, illustrated from [5].

(14)

Table 2.3: Data Ranges of Specific Conductivities and Relative Permittivity of Tissues at Low-Frequencies Specific conductivity Relative permittivity

Tumor 0.22–0.4 60 000 (at 1 kHz)

Fat 0.02–0.04 10 000 000 (at 10 Hz)

Muscle

Transversal 0.04–0.14 1 500 000–40 000 000(at 10 Hz) Longitudinal 0.3–0.8 10 000 000–66 000 000 (at 10 Hz)

Skin (dry) 0.00002–0.0002 1400–6600(at 10 Hz)

Stratum corneum 0.0000125 10 000 (at 2 Hz)

Lower-lying layers 0.227 1 200 000(at 2 Hz)

Bone 0.01–0.06 40000–1 000 000 (d.c.)

Blood 0.43–0.7 3000 (at 1 kHz)

Heart 0.06–0.4 7 000 000–20 000 000 (d.c.)

Kidney 0.6 30 000 000(d.c.)

Liver 0.023–0.2 15 000 000–50 000 000(d.c.)

Lung (inflated) 0.024–0.09 10 000 000 (d.c.)

Spleen 0.043 45 000 000 (d.c.)

Gray matter 0.033 50 000 000 (d.c.)

White matter 0.023 30 000 000(d.c.)

(Data obtained from [6])

Due to its safety and non- invasiveness, EBI has become the subject for many researchers and scholars. Though EBI is a simple measurement method it might suffer from severe measurement artifacts. One of the most commons artifacts as the known is capacitive leakage artifact of Hook effect.

2.5.1 Hook effect

Though the EBI measurement is simple, it has a commonly encountered artifact, i.e. Hook effect and in order to use it, the measurements have to be rid off this artifact. This effect is caused due to the capacitances at high frequencies. (Buendia, 2009)

2.5.1.1 Origin and its effect

The Hook effect usually is associated more to reactance than to resistance. It arises from the creation of a current divider circuit by an impedance measurement load with a parasitic capacitive pathway in parallel to each other. Parasitic capacitances are always present in any type of AC circuit and their influence, become critical at high frequencies.The Hook effect is named after its resemblance with the hook like shape in its impedance plot.

(15)

The Hook Effect must be corrected and compensated since it influences further analysis based of EBI, especially when doing Cole-based analysis and obtaining the Cole parameters, fittings and its estimations [4].

2.5.1.2 Correction and Compensation

To compensate the hook effect, the obtained EBI measurements are multiplied with an exponential factor, exp [-jωTd]. But this only compensates the phase error. This compensation method using a scalar Td is called Td compensation and it is well spread despite its limitation to compensate the estimation error in the module.

2.6 Cerebral monitoring

There are several ways of monitoring the brain, both invasively and non-invasively. Cerebral monitoring using EBI measurements belong to the non-invasively class. Several investigations have been carried out for the past 50 years, but for the past 20 years, extensive research work has been done on the EBI-based cerebral monitoring from it. In order to monitor the cerebral EBI measurements successfully, many issues come across that has to be taken care off like instrumentation, electrodes, measurement analysis, etc. It has been found that changes in EBI measurements occur when the brain suffers from injuries or cell swelling [7].

2.6.1 Cellular damage

The most sensitive tissue is the neural tissue because its functions depend on various metabolic pathways, oxygen supply, stress, genetics, surrounding environment and many more. Whenever the brain cells face these factors, they try to adapt themselves to get stability and this effort of it is called as dominated cellular adaptation. But this adaptations last only up to an extent and after that they suffer

Figure 2.5: The Hook effect to reactance (a) and phase (b)

(16)

2.6.2 Causes

The damages can have many reasons like insufficient oxygen, stress, insufficient blood, etc. but the most common among all is the injury caused by hypoxia, which is nothing but the loss of oxygen.

The most common origin of hypoxia is Ischaemia. Hypoxia is the condition faced when oxygen supply is insufficient to brain and Ischaemia is the condition where blood is insufficient. Lack of oxygen supply leads to cellular swelling and this condition is named as cellular Oedema [7].

2.6.3 Need for cerebral monitoring

As per the earlier studies and surveys, it can be inferred that the cerebral monitoring is very important for decreasing the death rate of the patients dying due to cerebral hemorrhage. Studies indicate that the cerebral damage occurs if neurons undergo injury, and then there arises a change in its electrical properties, thereby producing a change in EBI measurements of the brain. [5] The injuries can refer to oedema, hypoxia/ischaemia, perinatal asphyxia, etc. In order to avoid them, if EBI successful, EBI measurements could be used for brain monitoring- and early detection of brain damage.[8]

Figure 2.8: Intra cerebral hemorrhage

(17)

Chapter 3 FLOW OF ANALYSIS

3.1 EBI Spectroscopy Measurements

Complex EBI measurements obtained from 19 sick neonates have been analyzed. The measurements belong to two different groups, 12 out of 18 babies were born sick but show good outcome, and the other 7 did not recover and parish. The group with good outcome contained 293 measurement files and the group with bad outcome contained 230 measurement files.

Both set of files have been analyzed by fitting the data to the Cole extended model to get the best fittings. Using a standard error estimate parameter does the validation of the BIA equations in a sufficiently large number of subjects. The reason behind using this feature is that it is very safe for the patient. And by far, the complex studies related to the brain can be done easily by the EBI spectroscopy.

Thus, the best fittings were selected from each of the subjects and descriptive statistics were performed on them to characterize the sets.

3.2 Cole function fittings

The Cole parameters were obtained by fitting the EBI measurements to the Cole extended model using the batch-processing tool of the BioImp software. To perform a fitting the Bioimp software allows setting 3 different parameters: frequency range of the fitted data, the rejection limit of the EBI data considered for the fitting and the value of the parameter Td for Td compensation.

Since the data of this study contained several artifact and there was no method with valid scientific grounds to select the best parameters for each fittings. Therefore, a brute force fitting approach was used fitting the EBI data with several combinations of the 3 parameters according to the following list:

a) 5 Frequency ranges (2-450 KHz, 7-600 KHz, 12-525 KHz, 20-500 KHz, 40-450 KHz).

b) 2 Rejection limits (0%, 5%).

c) 5 Td correction values (0ns, 5ns, 10ns, 15ns, 20ns).

In this way, a total of 26150 files were obtained and were segregated for the analysis work.

3.2.1 Bioimp Software

The software used for the manipulation and fitting of the EBI measurements is the Bioimp

(18)

3.3 Filtering analysis

To ensure that all the data obtained with the Cole fittings were filter to remove inaccurate fittings and failed fittings. The obtained data were filtered according to filtering parameters contained in Figure 3.1.

When using BioImp the upper frequency limit of the Cole fitting process was set as high as 600kHz and all the measurements presented a characteristic frequency within the frequency limits of the selected frequency range, therefore no characteristic frequency over 600kHz must be produced;

According to the characteristics of Cole Model, the center of the semi-circle of the Cole plot must be always below the resistance axis, which means that the reactance center of the circle must be always smaller than zero. In addition, to filter all the fitting with a S.E.E value larger than 5% ensures that only accurate fittings are further analyzed.

3.4 MATLAB EBI manipulation and descriptive statistics

This section of analysis has been done by writing MATLAB scripts in order to analyze the obtained Cole fitted data. Especial attention has been paid to the analysis of the characteristic frequency.

3.4.1 Data processing in MATLAB

Each subject generated a histogram indicating the characteristic frequency values obtained with the Cole fittings. Only the subjects with certain even distribution of values around the centroid were selected for further analysis. After such filter, 9 sick subjects with good outcome and 6 acute subjects remain for further analysis. The next step is to select the 60% of the fittings producing a characteristic frequency value near the main lobe of the distribution. Finally, the measurement with the smallest S.E.E. value among for each of the subject was selected. All the selected measurements were stored in a file named Small_SEE. The final section of the analysis performing the descriptive statistics of the

Figure 3.1: Flow of data filtering in Excel

Filtered Data

SEE<5%

0<f_char<

600 kHz

X_centroid

<0Ω

Cole fitted Data

(19)

Cole parameters produces with the set of selected-files.

Note: As one of the important parameters of Cole model, the alpha parameter is not produced by the Bioimp software, the alpha parameter is calculated from the parameters of R0, R∞ and the radius of the obtained Cole plot as follows in the label (3.1).

^(3.1)

3.4.2 MATLAB functions

The analysis work in MATLAB was done with four functions. For the two groups of babies, the inputs and outputs are not the same when the same function is called.

3.4.2.1 Histogram creation

A histogram is generated for each subject by applying the MATLAB function hist (). One parameter should be calculated first, to obtain the number of bins-to represent the histogram. This is realized by calling the BIN_NUMBER () function. The character frequency values are the inputs and the main output is the number of bins when the bin size is equal to 1.

3.4.2.2 Subject selection

After the histograms were generated, subjects to be included for further analysis must be selected.

To decide which subjects remain for further analysis, the distribution of the values for the characteristic frequency is studied and compare with the average value. The CENTROID () function was called to calculate the centroid value of the distribution characteristic frequency values for each subject. The character frequency values and the variable conserving the number of data points in each segment were applied to acquire the centroid value. The function SUBJECT_SELECTION () was called when the centroid value had been obtained. A Boolean value was returned indicating that whether the centroid value is inside or outside the main distribution lobe.

3.4.2.3 Best measurement selection

In order to choose the best measurement, SELECTION () function was called. It performs the

Figure 3.2: Flow of data processing in MATLAB Centroid

fitting

60%

fitting

Smallest S.E.E Filtered

Data

Best Measurement

(20)

with a center frequency of 280 kHz and the 60% of the characteristic frequencies are distributed around the center value from 174 to 388, as indicated in Figure 3.3, only the fitting generated with a characteristic frequency within that range would evaluated for the best fit.

Figure 3.3: Schematic diagram presents the method to calculate the range of 60% for f_c

(21)

Chapter 4 RESULTS

This chapter presents the results obtained from the processing and analysis of the EBI data as presented in the previous chapter. Firstly, the histograms showing the distribution the values of the characteristic frequency obtained for the obtained Cole fittings for all the EBI measurements ARE PLOTED BY SUBJECT. Secondly, the histograms indicating the frequency range containing the 60%

of the fittings around the center frequency of the histogram are shown. And finally, the Cole parameters together with other impedance parameters from the selected best fittings are represented.

4.1 Histograms of f

char

for each subject

After filtering the Cole Fitting as indicated in section 3.4.2.3, different distributions of characteristic frequency were obtained for each subject. Figures 4.1 to 4.18 present the obtained histograms for all the 18 subjects.

In this section, the histograms with the characteristic frequency are shown for each neonate with good outcome.

4.1.1 Sick neonates with good outcome

The nine following figures include the histograms of the remaining subjects:

The distribution in this histogram looks like a Gaussian distribution with one main lobe. The centroid value equals to 283.03 kHz. The value at 0 kHz indicates those non-fit results

Figure 4.1: Histogram of obtained f_char for subject 008 with good outcome

0 100 200 300 400 500 600

0 2 4 6 8 10 12 14

Frequency(kHz)

Times

Baby008

******* Centroid

(22)

The shape of this histogram is similar like Gaussian distribution but most of the frequencies are located on the right side of the centroid. The centroid value is 159.73 kHz. One main lobe exists.

This histogram consists of several lobes spread over wide range and the centroid is at 154.95 kHz.

Subject 036 have four main lobes and several sides’ lobes. And the centroid locates at 85.78 kHz.

0 50 100 150 200 250 300

0 0.5 1 1.5 2 2.5 3 3.5 4

Frequency(kHz)

Times

Baby036

******* Centroid

0 100 200 300 400 500 600

0 1 2 3 4 5

Frequency(kHz)

Times

Baby032

******* Centroid

0 100 200 300 400 500 600

0 2 4 6 8 10 12 14

Frequency(kHz)

Times

Baby010

******* Centroid

(23)

Subject 041 only have one main lobe and centroid is at 59.12 kHz.

This characteristic frequency distribution has one main lobe. The centroid is at 95.04 kHz.

This histogram has one main lobe and many frequencies spread around it. Few frequencies are located away from this main lobe. The centroid is at 27.06 kHz.

0 50 100 150

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency(kHz)

Times

Baby045

******* Centroid

60 80 100 120 140 160 180

0 1 2 3 4 5 6 7 8 9

Frequency(kHz)

Times

Baby042

******* Centroid

Figure 4.5: Histogram of obtained fchar for subject 041 with good outcome

20 40 60 80 100 120 140

0 1 2 3 4 5

Frequency(kHz)

Times

Baby041

******* Centroid

(24)

The histogram distribution has a main lobe and all the frequencies are almost concentrated. The centroid is at 72.39 kHz.

In this histogram, many frequencies form a Gaussian distribution with only one main lobe. Few frequencies are outside and the centroid is 48.40 kHz.

Ideally, all figures should follow the Gaussian distribution. As many noise and interference exist everywhere in practice, it is difficult to obtain pure Gaussian distribution. Therefore, it is impossible to decide which kind of subjects can be left by comparing the shapes of the distribution for fchar. Another method to choose suitable subjects is to check the position of the centroid values. According to all the above figures, the centroid values are all placed among the first five peaks of fchar values. Subjects with such kind of centroid values can be remained for future analysis.

The following two subjects should be removed from further analysis as they have odd distributions:

0 50 100 150

0 2 4 6 8 10 12 14 16 18

Frequency(kHz)

Times

Baby057

******* Centroid

0 50 100 150 200 250

0 2 4 6 8 10 12

Frequency(kHz)

Times

Baby047

******* Centroid

(25)

Here, the main lobe is found to be at initial frequencies and a side lobe near the central frequencies. The centroid is 44.86 kHz, which is outside the first five peaks.

This histogram has only one main lobe and several spurious side lobes. However, the centroid valued 74.55 kHz is still outside the first five peaks.

4.1.2 Sick neonates with no recovery

This section will give all the histograms related to subjects that didn’t recover finally.

The first seven histograms belong to the subjects that will be left for next stage:

In this histogram, only one main lobe exists. The shape looks like a Gaussian distribution and the centroid is at 107.42 kHz.

Figure 4.12: Histogram of obtained f_char for subject 023 with acute sick

0 50 100 150 200 250 300 350

0 2 4 6 8 10 12

Frequency(Hz)

Times

Baby023

******* Centroid

20 40 60 80 100 120 140 160 180 200

0 2 4 6 8 10 12

Frequency(kHz)

Times

Baby051

******* Centroid

0 50 100 150 200 250 300 350

0 5 10 15 20 25

Frequency(kHz)

Times

Baby026

******* Centroid

(26)

This subject has a histogram with one main lobe and the centroid is at 101.53 kHz.

In this distribution, on the right side of the centroid (22.02 kHz), most frequencies exist and spread in a wider range than the other side.

This subject has only one lobe and intervals between peaks are quite large. The centroid is 32.04 kHz.

0 10 20 30 40 50 60 70 80 90

0 0.5 1 1.5 2 2.5 3

Frequency(Hz)

Times

Baby048

******* Centroid

0 10 20 30 40 50 60 70 80 90 100

0 5 10 15 20 25 30 35

Frequency(Hz)

Times

Baby034

******* Centroid

0 50 100 150 200 250 300

0 1 2 3 4 5 6

Frequency(Hz)

Times

Baby024

******* Centroid

(27)

The histogram of this subject contains one main lobe and several sides’ lobes. The centroid is 40.84 kHz.

This histogram looks like a perfect Gaussian distribution, with one main lobe at the centroid, i.e.

79.32 kHz.

The following figures represent the histograms of subjects with odd distribution of fchar values:

As this figure shows, the centroid value (62.25 kHz) of this subject does not fall in the range of

20 40 60 80 100 120 140 160 180

0 5 10 15 20 25 30 35 40 45

Frequency(Hz)

Times

Baby040

******* Centroid

20 40 60 80 100 120 140 160

0 1 2 3 4 5 6 7 8

Frequency(Hz)

Times

Baby063

******* Centroid

0 20 40 60 80 100 120 140 160 180

0 5 10 15 20 25

Frequency(Hz)

Times

Baby053

******* Centroid

(28)

changed, it is possible that this subject could be remained and used in further analysis.

It can be observed that the values for centroid are located the range of the first five peaks of fchar. In the two classes, totally 3 subjects have such kind of centroid values. These subjects were deleted from further analysis. However, the shapes of histograms should also be considered. If the histogram of a subject follows Gaussian distribution or looks similar, this subject could also be kept.

4.2 Histograms of the 60% of f

_char

In this section, figures indicate the 60% of the fittings producing a characteristic frequency value near the main lobe of the distribution. This range gives the most important and useful information of subject. The red star line in each figure indicates the best measurement.

4.2.1 Fittings for sick neonates with good outcome

The following figures indicate the figures of all remained 9 sick neonates with good outcome.

The histogram starts at 247.18 kHz (247 kHz in histogram) and ends at 381.44 kHz (381 kHz).

The value of the best measurement is 326.66 kHz.

This subject has the characteristic frequency range spanning from 113.05 kHz (113 kHz) to 247.32 (247) kHz. The frequency value for the best measurement is 225.18 kHz.

Figure 4.20: Histogram of the 60% of fchar for subject 010 with good outcome

100 150 200 250

0 2 4 6 8 10 12 14

Frequency(kHz)

Times

Baby010

******* Best messurement

Figure 4.19: Histogram of the 60% of f_char for subject 008 with good outcome

240 260 280 300 320 340 360 380 400

0 1 2 3 4 5 6 7

Frequency(kHz)

Times

Baby008

******* Best measurement

(29)

The histogram starts at 92.12 kHz (92 kHz) and ends at 255.21 kHz (255 kHz). 175.79 kHz is the frequency value for the best measurement.

In this histogram, the characteristic frequencies range from 43.21 kHz (43 kHz) to 151.86 kHz (151 kHz). The frequency value for the best measurement of this subject is 54.45 kHz.

This subject’s characteristic frequency distribution starts at 40.62 kHz (40 kHz) and ends at

40 45 50 55 60 65 70 75 80 85 90

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency(kHz)

Times

Baby041

40 60 80 100 120 140 160

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency(kHz)

Times

Baby036

80 100 120 140 160 180 200 220 240 260

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency(kHz)

Times

Baby032

(30)

Here, the characteristic frequency values of the subject starts at 80.08 kHz (80 kHz) and ends at 122.49 kHz (122 kHz). The best measurement’s character frequency value is 121.89 kHz.

The characteristic frequency values ranges from 20.33 kHz (20 kHz) to 41.42 kHz (41 kHz) with the best measurement’s frequency value being equal to 23.71 kHz.

This histogram starts from 46.00 kHz (46 kHz) to 114.24 kHz (114 kHz). The best measurement’s character frequency is 67.50 kHz.

40 50 60 70 80 90 100 110 120

0 1 2 3 4 5 6 7 8 9 10

Frequency(kHz)

Times

Baby047

20 25 30 35 40 45

0 0.5 1 1.5 2 2.5 3 3.5 4

Frequency(kHz)

Times

Baby045

80 85 90 95 100 105 110 115 120 125

0 1 2 3 4 5 6 7 8

Frequency(kHz)

Times

Baby042

(31)

In this histogram, the characteristic frequencies are from 37.03 kHz (37 kHz) to 67.04 kHz (67 kHz) and the best measurement’s characteristic frequency value is equal to 57.78 kHz.

4.2.2 Fittings for sick neonates without recovery

This section will display figures of those babies that didn’t recover.

The two edges of the histogram are 79.39 kHz (79 kHz) and 168.61 kHz (168 kHz). The characteristic frequency of the best measurement is 165.88 kHz.

The range of the characteristic frequencies is from 65.31 kHz (65 kHz) to 165.33 kHz (165 kHz).

Figure 4.29: Histogram of the 60% of f_char for subject 024 with acute sick

60 80 100 120 140 160 180

0 1 2 3 4 5 6 7 8 9

Frequency(Hz)

Times

Baby024

70 80 90 100 110 120 130 140 150 160 170

0 2 4 6 8 10 12

Frequency(Hz)

Times

Baby023

Figure 4.27: Histogram of the 60% of fchar for subject 057 with good outcome

35 40 45 50 55 60 65 70

0 2 4 6 8 10 12 14 16 18 20

Frequency(kHz)

Times

Baby057

(32)

In this histogram, the frequency range starts at 14.00 kHz (14 kHz) and ends at 40.23 kHz (40 kHz). The frequency of the best measurement is 15.37 kHz.

This characteristic frequency range starts from 25.34 kHz (25 kHz) and ends at 45.47 kHz (45 kHz). 39.20 kHz is the frequency of the best measurement.

The left edge and the right edge in this histogram are 27.16 kHz (27 kHz) and 73.10 kHz (73 kHz), respectively. The frequency of the best measurement locates at 31.23 kHz.

25 30 35 40 45 50 55 60 65 70 75

0 5 10 15 20 25

Frequency(Hz)

Times

Baby053

25 30 35 40 45 50

0 0.5 1 1.5 2 2.5 3

Frequency(Hz)

Times

Baby048

Figure 4.30: Histogram of the 60% of fchar for subject 034 with acute sick

10 15 20 25 30 35 40 45

0 5 10 15 20 25 30

Frequency(Hz)

Times

Baby034

(33)

The histogram indicates that the frequency range is from 56.68 kHz (56 kHz) to 108.98 kHz (108 kHz) with the frequency of the best measurement being at 79.82 kHz.

This histogram shows that the frequency range is from 46.03 kHz (46 kHz) to 90.06 kHz (90 kHz) and frequency value of the best measurement is 84.67 kHz.

For each subject, measurements whose characteristic frequency values are inside the 60% range were chosen for future analysis work. Other parameters of chosen measurements will be acquired and listed later.

4.3 Minimum S.E.E. criterion for best fitting analysis

The criterion to select the best fitting measurement has followed the minimum value for Standard Error of Estimate for the Cole fitting. The following two tables display the values of the Cole parameters, the characteristic frequency and other EBI parameters for the best-performed fit received for each subject of the two classes. The alpha values are also included in the tables.

45 50 55 60 65 70 75 80 85 90 95

0 5 10 15 20 25 30 35

Frequency(Hz)

Times

Baby040

******* Bestmeasurement

50 60 70 80 90 100 110

0 1 2 3 4 5 6 7 8

Frequency(Hz)

Times

Baby063

(34)

TABLE 4.1: PARAMETER VALUES OBTAINED IN THE ANALYSIS With Good Outcome

Subject X_centre R_centre Radius SEE R₀ R_∞ Z_char f_char α

008 -2.04 39.05 4.63 1.80 43.21 34.90 39.14 326.66 0.71

010 -9.63 47.22 14.03 1.12 57.42 37.03 47.43 225.18 0.52

032 -2.81 47.99 5.88 1.51 53.15 42.82 48.09 175.79 0.68

036 -6.79 41.20 8.80 1.25 46.80 35.60 41.25 54.45 0.44

041 -2.34 42.36 8.54 1.74 50.57 34.14 42.81 64.63 0.82

042 -9.81 41.36 20.16 1.05 58.97 23.75 42.64 121.89 0.68

045 -3.32 44.96 7.31 2.11 51.48 38.44 45.14 23.71 0.70

057 -5.80 44.71 8.53 1.83 50.96 38.45 44.79 67.50 0.52

057 -6.86 54.39 13.56 1.58 66.09 42.69 54.80 57.78 0.66

Mean -5.49 44.80 10.16 1.56 53.18 36.42 45.12 124.18 0.64

TABLE 4.2: PARAMETER VALUES OBTAINED IN THE ANALYSIS With Acute Sick

Subject X_centre R_centre Radius SEE R₀ R_∞ Z_char f_char α

023 -6.38 46.48 10.15 1.63 54.36 38.59 46.63 165.88 0.57

024 -3.61 37.66 9.31 1.42 46.24 29.08 38.09 151.41 0.75

034 -5.78 45.95 14.30 1.18 59.04 32.87 46.74 15.37 0.74

040 -6.26 41.63 11.90 1.14 51.75 31.51 42.01 84.67 0.65

048 -0.44 56.92 8.69 2.27 65.59 48.24 57.51 39.20 0.97

053 -1.49 47.29 6.69 1.94 53.82 40.77 47.58 31.23 0.86

063 -0.97 51.54 7.97 1.34 59.45 43.63 52.01 79.82 0.92

Mean -3.99 45.99 10.17 1.60 55.13 36.84 46.43 81.29 0.75

4.4 Reference values

After all the best measurements were selected, the maximum, minimum, mean and standard deviation values were calculated for all obtained parameters to get the impedance reference values.

Those values are shown in Table 4.3 and Table 4.4.

TABLE 4.3: ANALYSIS FOR OBTAINED PARAMETER VALUES With Good Outcome

X_centre R_centre Radius SEE R₀ R_∞ Z_char f_char α

Max -2.04 54.39 20.16 2.11 66.09 42.82 54.80 326.66 0.82

Min -9.81 39.05 4.63 1.05 43.21 23.75 39.14 23.71 0.44

Mean -5.49 44.80 10.16 1.56 53.18 36.42 45.12 124.18 0.64

SD 3.03 4.63 4.88 0.36 6.83 5.675 4.61 100.00 0.12

(35)

TABLE 4.4: ANALYSIS FOR OBTAINED PARAMETER VALUES With Acute Sick

X_centre R_centre Radius SEE R₀ R_∞ Z_char f_char α

Max -0.44 56.92 14.30 2.27 65.59 48.24 57.51 165.88 0.97

Min -6.39 37.66 6.69 1.15 46.24 29.08 38.09 15.37 0.57

Mean -3.99 45.99 10.17 1.60 55.13 36.84 46.43 81.29 0.75

SD 2.57 6.48 2.65 0.44 6.60 7.11 6.53 64.35 0.14

MEASUREMENTS COLE MODEL ANALYSIS F EBIS NEONATAL CEREBRAL

COLE MODEL ANALYSIS O F EBIS NEONATAL CEREBRAL

MEASUREMENTS

PRATHAMESH SHARAD DHANPALWAR

XINYUAN CHEN

Cole Model Analysis of EBIs Neonatal Cerebral Measurements

Dedicated

To Parents

&

Everyone Who Have Made This Possible

Prathamesh Sharad Dhanpalwar & Xinyuan Chen

29

October, Borås

Table of Contents

Chapter 1

INTRODUCTION

1.1 Introduction

1.2 Motivation

1.3 Goal

1.4 Work done

1.5 Structure

Chapter 2

ELECTRICAL BIOIMPEDANCE

2.1 Introduction

2.2 Electrical properties of tissues

2.3 Electrical equivalent of cell

2.4 Frequency dependent EBI

2.5 EBI measurements

2.6 Cerebral monitoring

Chapter 3

FLOW OF ANALYSIS

3.1 EBI Spectroscopy Measurements

3.2 Cole function fittings

3.3 Filtering analysis

3.4 MATLAB EBI manipulation and descriptive statistics

Chapter 4

RESULTS

4.1 Histograms of f

for each subject

4.2 Histograms of the 60% of f

4.3 Minimum S.E.E. criterion for best fitting analysis

4.4 Reference values

COLE MODEL ANALYSIS ^O F EBIS NEONATAL CEREBRAL