Introduction

Conventional clinical ultrasound imaging system assumes a pre-determined constant sound propagation speed, mostly 1540 m/s, in human soft tissue for the design of beam forming delay patterns. However, there are actually different sound speeds in different soft tissues. The mean values for different tissues range from 1420 m/s in breast fatty tissue up to about 1640 m/s in certain muscle tissue [1]. The mismatch between assumed and real sound speeds results in two potential degradations [2] in ultrasound image. A potential degradation is the spatial shift in ultrasound image because the assumed sound speed is used to calculate the distance between target and transducer. The other is the defocus of ultrasound image because both receive and transmit beam forming delay patterns are designed using the assumed sound speed. Sound speed estimation is not only can be used for improving imaging but also can be used for diagnosis. Even for same tissue, disease may cause different sound speeds. For example, sound speed of fatty liver is lower than normal liver. Thus, sound speed estimation not just can improve the quality of ultrasound image but also provide important diagnosis information.

There are various methods already proposed for sound speed estimation. Robinson et al. classified these methods into transmission and pulse-echo methods by principle [3]. Transmission methods measure sound wave propagation time between transmitter and receiver. Pulse-echo methods estimate sound propagation speed by processing pulse-echo data obtained from one or several ultrasound transducers. However most of them require multiple apertures or complex computation.

In this thesis, an average sound speed estimation method basing on lateral similarity focus quality factor is proposed. This method can estimate average sound speed for both homogeneous and two layer structures by finding the best focus quality ultrasound images formed by different assumed sound speeds. Furthermore, the possibility of fatty liver diagnosis using proposed method is proved by in vitro experiments for both fresh animal normal liver and fatty liver. Since homogeneous assumption, proposed method may be not stable to complex inhomogeneous structure. The performance of proposed method is under complex inhomogeneous structure is evaluated quantitatively by using PZFLex simulation. In this thesis, there are five chapters.

Sound speed estimation method

An average sound speed estimation method is proposed in this thesis using lateral similarity focus quality factor and basing homogeneous or multi layers homogeneous assumption. The lateral similarity can measure lateral speckle size. The presence of speckle is an inherent characteristic of medical ultrasound image. Speckle is formed as a result of the interference between echoes from nearby scatters. Since the speckle in ultrasound image is the convolution of point spread functions (PSFs) and scatterer reflectivity in complex plane with a random phase, the speckle size depends on PSF size. Thus lateral similarity can evaluate PSF size and focus quality. There are three steps in proposed method including receive beam forming, focus quality evaluation and iteration.

Firstly, different focus quality image can be formed using different assumed speeds. The PSF size will become larger when the sound speed mismatch increases since electronic focusing techniques are employed in most ultrasound imaging systems. In these techniques, both transmit and receive time delay patterns are designed to confirm that sound beam can focus on plan focus point. And they can be calculated as following,

where F is planned focus depth, N is number of active elements, n ranges from 1 to N, d is the center to center distance between adjacent elements and v is the sound propagation speed. As last equation shown, sound speed is an important parameter to calculate time delay patterns. If the sound speed mismatch increases, the time delay pattern error will become larger and sound beam will become wider in the plan focus depth. Thus the PSF size will become larger when the sound speed mismatch increases.

Secondly, the normalized acutocovariance function (NACVF) is employed for focus quality evaluation. Since NACVF can quantitatively evaluate speckle size, which depends on PSF size. It is able to evaluate PSF size and focus quality. Its expression can be written as following,

where ROI is the "region-of-interest", is the mean value of ROI, (x, u) and (z, v) are the lateral and axial coordinates, respectively. The NACVF in lateral direction is used to evaluate focus quality since PSF size in lateral direction is sensitive. Fig.1 shows lateral NACVFs of three images, which are formed by same pre-beam formed RF data using different assumed sound speeds. In this thesis, the average NACVF (ANACVF) of useful lateral shifts is employed to quantitatively evaluate focus quality of ultrasound image. The effect of noise can be reduced since average value of NACVFs of useful lateral shifts is used. Useful lateral shifts include all lateral shifts less than the maximum useful lateral shift. The maximum useful shift is decided by three steps. Firstly, the sound speed in the middle of the possible speed range is selected. Secondly, the NACVF curve of ultrasound image formed by the selected speed is calculated. Finally, if there is rebound before 30 lateral shifts, the rebound shift position is the maximum useful shift. If there is no, the maximum useful shift is 30.

Thirdly, Newton's iteration method is employed to find the best focus quality ultrasound images formed by different assumed sound speeds fast. Ultrasound image reconstruction times for sound speed estimation can be reduced obviously comparing to brute force method.

Evaluation

Performance of proposed method is evaluated quantitatively by both simulations and experiments. The evaluation includes homogeneous simulation, homogeneous and two layer phantom experiments, homogeneous and two layer in vitro experiments and complex inhomogeneous simulation. Firstly, homogeneous simulations are implemented by suing Field II simulation program. They show that absolute estimation errors of proposed method are 22.92±17.46 m/s (1.49%±1.13%), 4.57±2.83 m/s (0.30%±0.18%), 2.76±1.68 m/s (0.18%±0.11%), 1.50±0.87 m/s (0.10%±0.06%), 1.30±0.66 m/s (0.08%±0.04%) and 1.10±0.63 m/s (0.07%±0.04%) for ultrasound data obtained by 30, 50, 70, 90, 110 and 130 individual active elements, respectively and the performance of proposed method is obviously better than previous image registration and brightness methods. Secondly, homogeneous and two layer phantom experiments are implemented by using a homogeneous gel phantom and canola oil. They show absolute estimation errors of proposed method are 3.78±4.50 m/s (0.25%±0.30%) and 6.77±4.75m/s (0.45%±0.31%) for homogeneous and two layer phantoms, respectively. Thirdly, homogeneous and two layer in vitro experiments are implemented by using fresh normal liver, fresh fatty liver and canola oil. Homogeneous in vitro experiments show absolute estimation errors of proposed method are 5.59±5.68 m/s (0.36%±0.37%) and 6.93±3.57 m/s (0.47%±0.24%) for fresh normal and fatty livers, respectively. Two layer in vitro experiments show absolute estimation errors of proposed method are 8.79±4.08 m/s (0.57%±0.36%) and 9.79±3.75 m/s (0.66%±0.25%) for normal and fatty livers, respectively. Fourthly, complex inhomogeneous simulations are implemented by using PZFlex simulation software. They show that as the speed difference between background and inhomogeneous regions, the diameter of inhomogeneous regions and the percentage of inhomogeneous regions in sound field increase, the performance for proposed average speed estimation method decreases.

Discussion

In this thesis, an average sound speed estimation method is proposed and evaluations show its performance in both homogeneous and complex inhomogeneous structure and its possibility for fatty liver diagnosis. However, there are still several interesting future works for this study. First, performance of proposed method decreases when inhomogeneous region diameter increases since refraction. For large inhomogeneous region, refraction should be considered in receive beam forming for improving performance. Second, complex inhomogeneous simulation study just considers two dimension structure, but vivo tissue is three dimensions. Thus, three dimension complex inhomogeneous simulations will be an interesting future work. Third, all depth of ultrasound image is employed for focus quality evaluation, but defocusing of transmit focus depth is not sensitive to sound speed mismatch. Thus, different depth ultrasound image may be given different weight in focus quality evaluation for sound speed estimation. Fourth, ultrasound image analysis including segmentation and registration is heavily dependent on image quality. Ultrasound image analysis may be improved by using high quality ultrasound images formed by estimated sound speed.

Conclusion

In this thesis, there are mainly three contributions. First, an average sound speed estimation method is proposed by using lateral similarity focus quality factor. Second, fatty liver diagnosis possibility of proposed method is proved by using in vitro experiments. Third, performance of average sound speed estimation method under complex inhomogeneous is quantitatively evaluated.

Fig. 1 NACVFs of ultrasound images

従来の医療用超音波画像診断システムは,超音波ビームフォーミングの際,人体組織における音速を一定で仮定している.しかし,実際には人体の音速は組織によって異なる.この仮定と実際との差異は、空間的変位およびデフォーカスを生じさせ,超音波画像を劣化させる.また,同一組織においても,病変により音速が変化する場合がある.例えば,脂肪肝の音速は正常肝の音速より遅い一方,肝硬変になると音速は正常肝の音速より速くなる.このことから,生体組織における音速の推定により,超音波画像の劣化を補正するだけでなく,重要な診断情報の取得も可能である.本論文は生体組織での平均音速の推定により画像劣化の補正と,音速を用いた脂肪肝診断について研究したものである.

本論文では,超音波画像の横方向の相関を用いた,多層構造も対応可能な平均音速推定法を提案している.提案手法が重要な診断情報を提供することが可能であることを検証するため,脂肪肝診断を想定し,肝臓と脂肪の2層構造を模擬したin vitro実験で確認した.提案手法を用いた超音波画像の劣化補正を,ファントム実験およびin vitro実験で確認した.

第1章では,本論文の背景とイントロダクションを述べている.まず歴史および現在の医療用超音波イメージングについて紹介している.次に超音波ビームフォーミング時に用いる音速のミスマッチ問題について述べ,先行研究での平均音速推定法を紹介している.最後に,音速推定に基づいた病変診断について述べている.

第2章では,音速のミスマッチによる画像劣化について解析している.まず,超音波イメージング原理と方法を詳しく述べている.次に音速のミスマッチによる画像の空間的な変位および画像のデフォーカスについて理論的に分析している.

第3章では,音速推定に関する提案手法および従来手法を紹介している.まず,従来手法である画像レジストレーション法および輝度法について簡単に述べ,それぞれの利点と欠点について解析している.次に超音波画像の横方向の相関を用いた平均音速推定法を提案している.さらに,多層構造の対応方法を紹介している.最後に提案手法に反復アルゴリズムを組み合わせた,音速推定時間の短縮法について述べている.

第4章では,提案手法の検証のため,6つの実験及びシミュレーションを行っている.まず,手法の各段階での途中結果を示す.次に,音速が均一な組織の超音波画像をシミュレーションにより作成し,提案手法と従来手法の音速推定精度を評価し比較している.さらに,音速が均一なファントムを用いた実験及び,2層のファントムを用いた実験を行い,音速推定精度の評価を行っている.次に,動物の正常肝および脂肪肝を用いてin vitro実験を行っている.この実験では,まず直接肝臓の画像取得を行い,提案手法の評価を行った.次に対象を油に入れ,肝臓と脂肪の2層構造を模擬して評価した.提案手法で推定した正常肝の音速は1558.08±10.19 m/s, 脂肪肝の音速は1474.16±10.56 m/sであった. この結果から,推定した音速を用いた脂肪肝と正常肝の判別が可能であることを確認した.この結果は,提案手法を用いた脂肪肝診断の適用可能性を示している.次に,構造が複雑で不均質な物体における,提案手法の平均音速推定の精度評価を行っている.提案手法の推定精度が,(1)均一な背景と不均一な領域との音速差,(2)不均一な領域の直径および(3)不均一な領域の割合に影響されることがわかった.この実験では,構造が複雑で不均質な物体に対して,提案手法の精度を定量的に示した.最後に,提案する音速推定法を用いた超音波画像の空間的変位の補正について評価した.

第5章では,本研究の考察及び結論を述べている.

以上をまとめると,本研究では,超音波画像の横方向の相関に基づく,多層構造も対応可能な生体軟組織の平均音速推定法を提案した.肝臓と脂肪の2層構造を模擬したin vitro実験により,脂肪肝診断の可能性を確認した.また構造が複雑で不均質な物体に対して数値解析実験を行い,提案手法の適用限界を確認した.これらの成果より,本研究はバイオエンジニアリング分野に貢献していると判断できる.

よって本論文は博士(工学)の学位請求論文として合格と認められる.