Mikrodalgalar aracılığıyla biyolojik dokuların belirlenmesi
The determination of biological tissues through microwave
Yazar: MELİKE ERDOĞAN
Danışman: PROF. DR. İBRAHİM AKDUMAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı / Telekomünikasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Elektrik alan probu = Electric field probe ; Mikrodalga frekans = microwave frequence ; Teşhis = Diagnosis

Özet:
Bu tez çalışmasında, tibbı tanı kiti olarak tasarlanacak olan açık uçlu koaksiyel mikrodalga probun elektromanyetik modeli, çalışma prensibi ve malzemenin elektromanyetik özelliklerini bulmak ve sınıflandırma yapabilmek için kullanılan yöntemler anlatılmıştır. Sonrasında, bir takım örnek veriler üzerinde bu algortimaların kullanılıp kullanılamayacağı denenmiştir. Bu sonuçlar elde edilen hata oranlarına göre değerlendirilerek bir sonuca varılmıştır.
Malzemenin elektromanyetik davranışı kendine özgü olan dielektrik geçirgenliği, manyetik geçirgenliği ve iletkenlik katsayısı ile modellenebilir. Bu katsayıların bulunması malzemeyi tanımlamak için yeterlidir. Manyetik olmayan malzemelerde (örneğin: canlı dokusu) dielektrik geçirgenliğin ve iletkenliğin bulunması modelleme için yeterlidir. Bundan dolayı, açık uçlu mikrodalga koaksiyel prop malzemenin bu özelliklerini bulmak için kullanılanılacaktır.
İlk olarak, malzemelerin belirtilen özelliklerini bulmak için açık uçlu koaksiyel prob ile malzemenin yansıma katsayısı ölçülecektir. Bu ölçüm düzeneği; ölçülecek malzeme, prob, kablo ve VNA'den oluşmaktadır. Böylece, bir mikrogalda devresi kurulur. VNA ile probun ucu arasındaki kullanılan malzemelerin oluşturacağı kayıbın etkisini azaltmak için kalibrasyon yapılmalıdır. Kalibrasyon işlemi sonunda ölçülen yansıma teriminden probun ucundaki yansıma katsayısına, hesaplamalarda kullanılacak olan, geçilmiş olur. Kalibrasyon sonucunda elde edilen yansıma katsayısından malzemenin admitansı bulunur. Admitans değeri ile malzemenin elektriksel katsayıları arasındaki ilişkiden istenen dielektrik geçirgenliğe ve iletkenlik katsayısına geçilir. Bu  hesaplamalar açık uçlu mikrodalga koaksiyel probun admitans modeli kullanılarak yapılacaktır. Fakat, malzemenin admitansından dielektrik katsayılarına geçme problemi iyi tanımlanmamış bir problem olduğu için direk çözülememektedir. Çözüm için Gauss-Newton İteratif yöntemi kullanılacaktır. 
Gauss-Newton yöntemi ile karmaşık sayı olarak malzemenin dielektrik katsayısı bulunur. Bu karmaşık sayının gerçek kısmı dielektrik geçirgenlik, sanal kısmından ise iletkenlik katsayısına geçilir. Ayrıca, bu katsayılar ölçüm yapılan frekansa bağlı olarak değişmektedir. 
Ölçüm için kullanılmış VNA 500 MHz - 6 GHz arasında 500 MHz aralıklarla 12 noktada değer vermektedir. Dolayısıyla elde edilen verinin boyutu, ölçüm miktarı N olmak üzere, (N X 12) şeklinde olacaktır. Bu verinin boyutu çok büyük olduğu için öncelikle daha düşük boyutlara indirilecektir. Boyut düşürme işlemi için makine öğrenmesi yöntemlerinden biri olan temel bileşen çözümlemesi (PCA) yöntemi kullanılacaktır. Bu yöntem ile verinin boyutu iki boyuta indirililebilmiştir. Bunun için de veri matrisinin özdeğer ve özvektörleri kullanılacaktır.
İki boyutlu yeni veriyi bir başka makine öğrenmesi algoritması olan SVM algoritmasına girilecektir. SVM uzman denetimine ihtiyaç duyan bir algoritmadır. Ölçülen veriler bir uzman kontrolünde bir kısmı pozitif, '+', bir kısmı  negatif, '-', olarak etiketlenir ve sisteme öğretilir. Algoritmanın oluşturduğu ayrıma göre alınan diğer ölçümler üzerinde sınıflandırılma yapılacak ve hata oranlarına göre bir sonuç çıkarılacaktır.
Cerrahpaşa Tıp Fakültesinde Prof. Dr. Tunaya Kalkan tarafından fare karaciğerleri üstünde yapılmış ölçümlerde tümörlü ve sağlıklı dokuların dielektrik geçirgenliği ve iletkenlik katsayıları bulunmuş ve bu veriler paylaşılmıştır. Bunlardan yararlanarak ölçüm değerleri arasında ayrım yapılabilecek bir fark bulunmaya çalışılmıştır. Sonuç olarak yapılan çalışmalar neticesinde, bu verilerin çoğunlukla ayrıldığı ve sınıflandırmaya uygun olduğu gözlenmiştir. Dolayısıyla, bu algoritmanın bunun gibi doku tespiti türündeki ileri çalışmalarda kullanılabileceği öngörülebilmektedir.

Abstract:
In this thesis study, an open-ended coaxial microwave probe is designed to use for medical diagnostic kit. Also, the electromagnetic model and working principle of the probe and the methods, which used to find the electromagnetic properties of the materials and to classify these data are explained clearly in this thesis study. Then, the application of these algorithms are tested on a set of sample data. It has been reached a conclusion through evaluation of results which obtained error rates and figures.
Electromagnetic behavior of each materials are modelled by a unique relative permittivity, relative permeability and conductivity coefficients.  If these coefficients will be found, it can be sufficient to define a material. Moreover, finding relative permittivity and conductivity is enough for modelling the non-magnetic materials (for example: organism tissue). Therefore, we will use an open-ended microwave coaxial probe to find the relative permittivity and conductivity of any tissues.
Firstly, admittance of any material will be calculated from the open-ended coaxial probe measurements to achieve the relative permittivity and conductivity of it. Admittance value can be found from the measurement of the reflection coefficient at the end of the probe. However, we cannot obtain the value of reflection coefficient at the first step, due to the measurement setup, which contains probe, cable, connector and VNA (vector network analyzer). We have to do the calibration to get the requested reflection coefficients.
This calibration procedure consist of the measurements of three different reflection coefficient at the probe port or dielectric coefficients known materials. The reflection coefficients known short and open circuit conditions are practical for two of them. Latter, one more measurement has been done with the water, which is known as the dielectric coefficients. It is suggested that the reflection coefficient of an unknown material is calculated in between the relationships of the three measurements' known reflection coefficient and measured reflection terms. Thus, the calibration ended through finding the reflection coefficients. The admittance can also be gathered from these coefficients.
The main problem is that the dielectric properties of the material is obtained by the admittance value. This problem is solved with using the admittance model of the open-ended coaxial probe. In this model, an equation give the admittance value depending on the relative permittivity and conductivity. However, finding these coefficients from the admittance is an ill posed problem. Due to this ill posed problem, it could not be solved directly. Therefore, the Gauss-Newton Iteration is chosen to apply to the admittance values and the relative permittivity and conductivity coefficients are obtained. Besides, these coefficients depend on the measurement frequencies. 
We use some sample data measured with working at 500 MHz - 6 GHz bandwidth VNA. Measurements also were taken at 12 points with 500 MHz range. The dimension of the data become (N x 12), including N is measurement number. The principal components analysis (PCA) method is primarily used to reduce the data size which is quite huge. 
PCA is not only one of machine learning algorithms, but also the most common feature extraction algorithm. In addition, it is an unsupervised method and it does not use the output information. This algorithm is used to find a mapping with the dimension of input data to the lower dimension, according to the data matrix's eigenvalues and eigenvectors. In algorithm, initially it takes the variance of input dataset. After taking the covariance of data, the eigenvalues of new dataset is checking about values of them. Mostly, there is one or two eigenvalue(s) is more dominant than other eigenvalues. Dominant ones are called principal component, and these eigenvalues corresponds to the component of data matrix relevant with their eigenvectors. Therefore, we can define all data in these two vectors. Our multi-dimensional dataset, the dimension of it is (Nx12), is entered into PCA and on the same way we can gather the desired vectors. Although, in our problem, there is one dominant eigenvalue, it can be featured in two dimension, because of our complex dataset. First eigenvalue become dominant corresponding to the first component of data matrix is chosen. This data vector consists of complex numbers, so first dimension is real part of the vector, second dimension is imaginer part of it. Then, this new two dimensional data is entered into the Support Vector Machine (SVM) method to try to find out any differentiation related measurement results.
SVM is also a kind of machine learning algorithms, unlike PCA it is a supervised method. This method is used for classification and regression analysis. In this algorithm, an expert labels all data independent from the value of data. Some of data is labelled as 'x', the other part labelled as 'o'; also the algorithm is trained with this labelled data. The algorithm is trying to determine a divide line according to the distances between the chosen support vectors through both labelled 'x' and 'o' data. When the algorithm selects which data point is support vector, the kernel function has played an important role. After the line is determined, the values come from the new measurements are tested and classified by this system. Even though SVM can classify high-dimensional feature spaces, we do the classification just in two dimensions with the output of PCA.
The main purpose of this thesis study is that finding a difference between the dielectric properties of healthy and malignant tissues. According to this, we have the relative permittivity and conductivity coefficients of tumor and healthy tissues of rats' liver measurements data, which be taken by Prof. Dr. Tunaya Kalkan at Cerrahpasa Medical Faculty. Besides, there is two types of measurement setup. In the first one, before the tissues are measured with the probe, they are wetted by a liquid, named normal saline not to dry them. In a second one, also they are wetted by it, after that, they are wiped with the cotton. In this way, not only it prevents the tissues from getting dry, but also the dielectric properties of them are conserved. These two types of datasets are respectively entered into PCA and SVM algorithms. After that, all data is gathered in one and entered into these algorithms. The outputs of the SVM contain figures and error rates. The figures are evaluated for the visual examination. Otherwise, the error rates are numerical results to show the real performance of our proposal approach.
In both first and second measurement setups, the data samples were taken from two groups rats. First group consisting of healthy rats is control group; second one is experimental group consist of unhealthy rats. The samples of control group are labelled as healthy data. Although they are obtained from the experimental group, not all samples have tumor node so, the experimental group's samples involved two different data; one of them is labelled as tumor data, the other is normal tissue samples. Tumor and healthy tissues set are managed to train SVM algorithm. Separating line is determined with these sets. In addition, normal tissues taken from experimental group are used for testing the algorithm.
In first measurement setup, the division between the tumor and healthy tissues taken with normal saline are found with 18,10% error rate. In second measurement setup, the difference of these data set is done with 8,10% error rate. Furthermore, the figures, which the visual results of these setups are, support these error rates. When comparing these results, the second setup is getting better and more stable results than the first one. Then, the experimental group's normal samples test with SVM train set, just so these results have worse error rates about 70%. However, it must be remembered that these samples are obtained from the unhealthy rats; in this way, it is possible that these samples could be tumor tissue. Therefore, it is necessary that the data samples should be controlled with the pathology report. Thereafter, all of control group's healthy data and experimental group's tumor data of two measurement setups are gathered in two data sets. These steps, PCA and SVM are also applied to this data sets. The performance of this last division reach 84% percent. Normal samples are also tested with SVM result such that it is getting 72% error rate.
Consequently, when we compare these results, these data sets are mostly separable and suitable for classification. So as, it is predictable that this algorithm work in this type of analysis can be used in tissue. Also, this results show that this new proposal approach can be applied on new data samples as a subject of a new study.