超音波逆散射訊號之統計模型與應用

The Statistical Model and Application of Ultrasonic Backscattering signal

蔡富全(Fu-Chuan Tsai)

指導教授 ： 王士豪

中原大學/工學院/醫學工程研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100417

摘要

超音波逆散射統計模型已使用於許多組織之特性化上，例如肝、腎以及乳房等組織。當在sample volume內的散射子為fully developed的狀態時，其散射訊號包封之機率密度函數(PDF)會成Rayleigh分佈，但組織內大都不符合fully developed的狀態，因此便衍生許多non-Rayleigh模型更能有效的描述超音波散射訊號，例如K模型。但由於其複雜性以及參數須在一定範圍內才較具意義，在此我們使用包含更廣闊散射子條件且較簡單的Nakagami模型來描述骨骼的逆散射訊號，並與上述模型做比較。
本研究使用1 MHz超音波換能器來進行人體脛骨與跟骨測量，儲存其散射訊號以便進行進一步分析，並藉由SNR、高階moment、K參數、Nakagami參數等來作為骨質定量之參數。
透過軟體模擬可驗證統計參數與散射子濃度之關係，並且藉由血液實驗與相關文獻確認本實驗之正確性。利用摻雜玻璃細砂的洋菜假體模擬在resolution cell內含有強散射子之狀態，結果顯示SNR值大於1.91，m值大於1，其散射訊號包封之PDF為post-Rayleigh分佈。在假體實驗中，Nakagami模型相較於Rayleigh模型有較小之LSE。
量測的骨骼組織包含正常人及骨質疏鬆病患之脛骨與跟骨，結果顯示正常人SNR、m值在脛骨呈中央高、脛骨兩端與跟骨較低之趨勢。骨質疏鬆病患並無一定的趨勢，而且在脛骨兩端與跟骨之SNR值與m值均大於正常人之值，其它的參數範圍值也與正常人不同。經比較各種模型結果後，Nakagami模型對於骨質流失產生強散射子所引起之post-Rayleigh分佈有較好之描述特性。

關鍵字

散射訊號 ； K分佈 ； Nakagami分佈 ； 骨質疏鬆

並列摘要

Ultrasonic backscattered signals analyzed using statistical models have applied to characterize tissues, such as liver, kidney, breast, etc. When scatterers in the sample volume is distributed to be fully developed, the probability density function (PDF) of the backscattered envelop will be Rayleigh distribution. Most of scatterers in tissues however is not fully developed. Thus, other models ( such as K distribution ) were adopted to better describe properties of ultrasonic backscattered signals. Due to the complex nature of K distribution and that it is meaningful only in certain conditions, Nakagami model which could include more generalalized scatterer conditions and is easier was used to describe the backscattered signals of the bone tissues. Results were compared with those from previous models.
A 1 MHz transducer was used to performed measurements from human tibia and calcaneus. Backscattered signals were stored for further analysis. Parameters including such as SNR, high order moments, K parameter, Nakagami parameter were applied to quantify the bone mass. Simulation was also carried out to verify the relationship between parameters and scatterers concentration. The accuracy of the experimental method was validated by comparing current results from blood experiments with those of previous studies. Phantom made by the agar containing glass beads was to simulate the condition with strong scatterers in resolution cell. Experimental results obtained from phantoms show that the SNR of backscattered signals is above 1.91, the m parameter is above 1, and the PDF of the backscattered envelop is post-Rayleigh dostributed. Nakagami model has smaller least-square-error (LSE) than Rayleigh model obtained from phantom experiments.
Bone tissues including the tibia and calcaneus from healthy people and osteoporosis patient were then measured. The value of SNR and m parameter is larger in the middle position of the tibia than those collected from two ends and calcaneus. There is no regular distribution of either SNR or m parameters from patients. The value of SNR and m parameter from patients in the other two ends of tibia and calcaneus is always larger than those acquired from healthy people. The other parameters obtained from patients are also different from those of healthy people. Compared with all models, Nakagami model has better capability to characterize the post-Rayleigh distribution according to strong scatterers caused by the loss of bone mass.

並列關鍵字

K distribution ； scattering signal ； Nakagami distribution ； Osteoporosis

參考文獻

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