臺灣博碩士論文加值系統

不同性質的散射子會對於來自生物組織的超音波逆散射包封訊號造成不同的統計分布特性。這些具有不同統計分布特性的包封訊號可透過一個能涵蓋所有超音波散射情形的Nakagami統計模型來描述其機率密度函數，其中Nakagami參數又對於區分生物組織散射子濃度的變化具有良好的能力。為了擁有Nakagami參數在定量生物組織特性時更佳的執行效能，我們探討了換能器效應、雜訊效應、以及對數壓縮效應在Nakagami參數估計時所可能造成的影響，同時也評估以Nakagami模型為基礎的參數運用在血液濃度偵測的可行性。
首先進行假體實驗與二維電腦模擬以探討換能器效應對於Nakagami參數估計的影響。使用中心頻率為5 MHz的非聚焦式與聚焦式換能器擷取散射子濃度由2至32 scatterers/mm3的假體超音波逆散射訊號。以相同的電腦模擬方法進一步探討在相同散射子濃度範圍內，雜訊與對數壓縮對於Nakagami參數估計之效應。最後以5 MHz的聚焦式換能器擷取來自血容比範圍由3%至50%的紅血球懸浮液，以此評估使用Nakagami統計模型的參數辨別血容比之可行性。
實驗結果證明，以聚焦式換能器所估計的Nakagami參數相較於使用非聚焦式換能器所估計的參數擁有更高的靈敏度以偵測散射子濃度的變化。Nakagami參數區分不同散射子濃度的靈敏度會隨著逆散射訊號訊雜比的下降而降低。此外，對數壓縮的計算會將大多數散射子濃度所相對應的包封訊號統計移至post-Rayleigh分布，使得透過壓縮的逆散射包封來估計的Nakagami參數具有更佳的靈敏度以區分不同的散射子濃度。另一方面，以未經壓縮的超音波逆散射包封所估計的Nakagami參數並無法區分不同的血容比，原因在於這些不同濃度的包封訊號統計皆為Rayleigh分布。然而，在經過對數壓縮的計算之後，所得到的Nakagami參數可有效的辨別血容比的變化。本研究結論，Nakagami參數在組織特性化中較佳的執行效能可在使用良好聚焦的換能器以及低雜訊干擾的情況下獲得。可用來提昇Nakagami參數靈敏度的對數壓縮技術，亦可幫助超音波逆散射統計參數進一步的應用於未來非侵入式血容比測量技術的發展與推廣。

Various properties of scatterers may cause different statistical distributions for the envelopes of ultrasonic backscattered signals received from biological tissues. The Nakagami statistical distribution, which has been demonstrated to be a general model capable of encompassing all conditions of ultrasonic backscattering, was proposed to describe the probability density function (PDF) of ultrasonic envelope signal. In particular, the Nakagami parameter estimated using the backscattered envelopes has a good ability to distinguish the variation of scatterer concentration in tissues. For the better performance of the Nakagami parameter in quantifying the properties of biological tissues, the effects of transducer characteristics, noise, and logarithmic compression on the estimation of the Nakagami parameter were explored. The feasibility for the application of the Nakagami-model-based parameters to the detection of blood concentration was also evaluated in this study.
The measurements of phantoms and two-dimensional computer simulations were carried out to explore the effects of transducer characteristics on the estimation of the Nakagami parameter. The Nakagami parameter as a function of scatterer concentration was calculated using backscattered signals acquired from the scattering medium of different scatterer concentrations ranged from 2 to 32 scatterers/mm3 using both 5 MHz non-focused and focused transducers. The same simulation method was further applied to produce the 5 MHz backscattered echoes in the same range of scatterer concentration to investigate the effects of noise and logarithmic compression on the Nakagami parameter estimation. The ultrasonic signals backscattered from red cell suspensions with hematocrits ranging from 3% to 50% were collected using a 5 MHz focused transducer to further verify the feasibility of the hematocrit differentiation by the parameters of the Nakagami distribution.
The results demonstrated that the Nakagami parameter estimated using a focused transducer tends to be more sensitive than that by a non-focused transducer to detect the variation of the scatterer concentration. Moreover, the sensitivity of the Nakagami parameter to differentiate different scatterer concentrations would decrease gradually corresponding to the decrease of signal-to-noise ratio (SNR) of backscattered signals. In addition, the logarithmic compression would move the statistics of the backscattered envelopes toward post-Rayleigh distributions for most scatterer concentrations, making the Nakagami parameter calculated using compressed backscattered envelopes is more sensitive than that calculated using uncompressed envelopes in differentiating variations in the scatterer concentration. On the other hand, the Nakagami parameter calculated using the uncompressed backscattered envelopes cannot be used to separate various hematocrits due to that the probability distributions of the uncompressed envelopes of different hematocrits all follow Rayleigh statistics. However, different hematocrits can be effectively distinguished using the Nakagami parameter after applying logarithmic compression to the envelope signals. This study concluded that the better performance of the Nakagami parameter in characterizing tissues could be achieved in conditions with both the use of well-focused transducer and the low noise interference. The logarithmic compression that assists in the enhancement of the Nakagami parameter sensitivity has a great potentiality in the future development of a new method to measure the hematocrit based on the Nakagami model.

TABLE OF CONTENTS

中文摘要 i
ABSTRACT iii
ACKNOWLEDGEMENTS v
TABLE OF CONTENTS vi
LIST OF FIGURES ix
LIST OF TABLES xii
CHAPTER 1. INTRODUCTION 1
1.1 General 1
1.2 Ultrasonic tissue characterization using backscattering statistics 3
1.3 Research objectives 5
1.4 Dissertation organization 7
CHAPTER 2. THEORETICAL BACKGROUND 9
2.1 Fundamentals of wave propagation 9
2.2 Reflection, refraction, and attenuation 11
2.3 Scattering of objects 15
2.4 Statistical models used to describe the backscattered statistics 18
2.4.1 Rayleigh distribution model 18
2.4.2 Rician-distribution-based models 21
2.4.3 K-distribution-based models 23
2.4.4 Nakagami distribution model 25
CHAPTER 3. EFFECTS OF TRANSDUCER CHARACTERISTICS ON THE ESTIMATION OF NAKAGAMI PARAMETER 29
3.1 Introduction 29
3.2 Experiments on phantoms 29
3.2.1 Preparation of phantoms 29
3.2.2 Experimental arrangement and procedure 31
3.3 Computer simulations 33
3.3.1 Model of ultrasonic backscattered signals 33
3.3.2 Simulation procedure 34
3.4 Results 37
3.5 Discussion and conclusions 52
CHAPTER 4. EFFECTS OF WHITE NOISE ON THE ESTIMATION OF NAKAGAMI PARAMETER 55
4.1 Introduction 55
4.2 Computer simulations 56
4.3 Results 57
4.4 Discussion and conclusions 66
CHAPTER 5. EFFECTS OF LOGARITHMIC COMPRESSION ON THE ESTIMATION OF NAKAGAMI PARAMETER 69
5.1 Introduction 69
5.2 Principle of logarithmic compression 69
5.3 Computer simulations 71
5.4 Results 72
5.5 Discussion and conclusions 84
CHAPTER 6. APPLICATION OF NAKAGAMI PARAMETERS TO DIFFERENTIATION OF HEMATOCRIT 88
6.1 Introduction 88
6.2 Experiments on red cell suspensions 89
6.2.1 Preparation of suspensions 89
6.2.2 Measurement arrangement and method 90
6.3 Results 94
6.4 Discussion and conclusions 102
CHAPTER 7. CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 106
7.1 Conclusions 106
7.1.1 Effects of transducer characteristics on estimation of m parameter 106
7.1.2 Effects of noise on estimation of m parameter 107
7.1.3 Effects of logarithmic compression on estimation of m parameter 107
7.1.4 Feasibility for hematocrit differentiation 108
7.2 Suggestions for future work 109
REFERENCES 111
PUBLICATION LIST 122



LIST OF FIGURES

Fig. 2.1 Reflection and refraction of the plane wave at the boundary between medium I with the acoustic impedance Z1 and medium II with the acoustic impedance Z2. 14
Fig. 2.2 Illustration for ultrasonic scattering. 16
Fig. 2.3. The Nakagami probability functions for different values of m. 28
Fig. 3.1. Photo for the particles used in the experiments. 30
Fig. 3.2. Experimental arrangement. 32
Fig. 3.3. Display of 2-D simulated incident wave. 35
Fig. 3.4. Pulse echo impulse responses (left) and spectra (right) of 5 MHz transducers. (a) and (b) non-focused transducer; (c) and (d) focused transducer. 38
Fig. 3.5. Lateral (left) and axial (right) profiles of 5 MHz transducers. (a) and (b) non-focused transducer; (c) and (d) focused transducer. 39
Fig. 3.6. Simulated pulse echo impulse responses (left) and spectra (right) of 5 MHz transducers. (a) and (b) non-focused transducer; (c) and (d) focused transducer. 41
Fig. 3.7. Simulated power density patterns of main lobes in the far-field. 42
Fig. 3.8. Typical experimental (left) and simulated (right) backscattered signals acquired from the scatterer concentration of 2 scatterers/mm3. (a) and (b) non-focused transducer; (c) and (d) focused transducer. 43
Fig. 3.9. The Nakagami parameter as a function of scatterer concentration estimated using a 5 MHz non-focused transducer. 44
Fig. 3.10. PDFs of backscattered envelopes of different scatterer concentrations measured using a 5 MHz non-focused transducer. (a) 2 scatterers/mm3; (b) 32 scatterers/mm3. 45
Fig. 3.11. The Nakagami parameter as a function of scatterer concentration estimated using a 5 MHz focused transducer. 46
Fig. 3.12. PDFs of backscattered envelopes of different scatterer concentrations measured using a 5 MHz focused transducer. (a) 2 scatterers/mm3; (b) 32 scatterers/mm3. 47
Fig. 3.13. The Nakagami parameter as a function of scatterer concentration simulated using a 5 MHz transducer. (a) non-focused transducer; (b) focused transducer. 49
Fig. 3.14. PDFs of backscattered envelopes of different scatterer concentrations simulated using a 5 MHz non-focused transducer. (a) 2 scatterers/mm3; (b) 32 scatterers/mm3. 50
Fig. 3.15. PDFs of backscattered envelopes of different scatterer concentrations simulated using a 5 MHz focused transducer. (a) 2 scatterers/mm3; (b) 32 scatterers/mm3. 51
Fig. 4.1. A typical white-noise signal (a) and its spectrum (b) in the simulations. 58
Fig. 4.2. The PDF and curve fitting using the Nakagami parameter for the white noise envelope obtained in the simulations. 59
Fig. 4.3. The simulated results without any noise interference. (a) A typical backscattered signal; (b) The Nakagami parameter as a function of scatterer concentration. 60
Fig. 4.4. The simulated results for both typical backscattered signals (left) and the Nakagami parameter as a function of scatterer concentration (right) for the following SNR values: (a) 40 dB; (b) 20 dB; (c) 10 dB; (d) 5 dB; and (e) 0 dB. 63
Fig. 4.5. The Nakagami parameter as a function of SNR for different scatterer concentrations. 64
Fig. 4.6. The sensitivity of the Nakagami parameter as a function of SNR. 65
Fig. 5.1. The PDF of the backscattered envelopes and its curve fitting by the Nakagami model. (a) 2 scatterers/mm2. (b) 32 scatterers/mm2. 73
Fig. 5.2. The m parameter as a function of scatterer concentration. 74
Fig. 5.3. The PDF of the compressed backscattered envelopes (D = 1) and its curve fitting by the Nakagami model. (a) 2 scatterers/mm2. (b) 32 scatterers/mm2. 77
Fig. 5.4. The mlog parameter as a function of scatterer concentration (D = 1). 78
Fig. 5.5. The PDF of the compressed backscattered envelopes (D = 2) and its curve fitting by the Nakagami model. (a) 2 scatterers/mm2. (b) 32 scatterers/mm2. 79
Fig. 5.6. The PDF of the compressed backscattered envelopes (D = 3) and its curve fitting by the Nakagami model. (a) 2 scatterers/mm2. (b) 32 scatterers/mm2. 80
Fig. 5.7. The mlog parameter as a function of scatterer concentration (D = 2) 81
Fig. 5.8. The mlog parameter as a function of scatterer concentration (D = 3) 82
Fig. 6.1. The experimental setup for the measurement of ultrasonic backscattering from red cell suspension. 93
Fig. 6.2. The Ω parameter as a function of hematocrits ranging from 3% to 50%. Mean and SD values are shown. 95
Fig. 6.3. The Ωlog parameter as a function of hematocrits ranging from 3% to 50%. 96
Fig. 6.4. The PDFs of uncompressed backscattered envelopes and curves fitted by the Nakagami model for different hematocrits: (a) 3%; (b) 12%; (c) 50%. 98
Fig. 6.5. The m parameter as a function of hematocrits ranging from 3% to 50%. 99
Fig. 6.6. The PDFs of compressed backscattered envelopes and curves fitted by the Nakagami model for different hematocrits: (a) 3%; (b) 12%; (c) 50%. 100
Fig. 6.7. The mlog parameter as a function of hematocrits ranging from 3% to 50%. 101


LIST OF TABLES

Table 3.1. Characteristics of the non-focused and focused transducers. 37
Table 4.1. Values of non-linear regression parameters for the Nakagami parameter in Fig. 4.5 as a function of SNR with the equation of , where r is the correlation coefficient. 66
Table 5.1. The mean and standard deviation values of the m and mlog parameter for scatterer concentrations ranging from 2 to 32 scatterers/mm2. 83
Table 6.1. Chemicals and materials for the preparation of ACD solution. 90

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