統計模型被廣泛應用於描述超音波逆散射包封訊號的機率密度函數，而超音波逆散射包封訊號的統計模型可定量分析生物組織特性。由於超音波能量的衰減會隨著頻率的增加而上升，導致回波訊號變形，影響統計參數的分析。因此本研究探討超音波頻率、激發週期與衰減效應對超音波逆散射包封訊號機率密度函數的影響。實驗使用3.5及7.5 MHz聚焦式換能器量測散射假體，散射假體為混合吉利丁與不同濃度的玻璃珠(直徑為30~50 μm)所製作，分別是16與 64 顆散射子/mm3；衰減效應是利用在換能器與散射假體之間擺放不同厚度的矽膠片分別為0、0.1、0.2與0.3 mm。超音波換能器分別以1、3、5與10個週期的弦波訊號激發，此研究顯示當以一個週期的弦波訊號激發換能器時，會使得Nakagami參數明顯受到衰減效應的影響。在頻寬的效應下，隨著激發週期的上升頻寬越趨近於窄頻而抑制衰減效應，尤以三個週期的弦波訊號可以保留較好的軸向解析度與有效抑制衰減效應。Nakagami參數隨著散射子濃度、激發的週期數、衰減效應的增加而有遞增的趨勢。

Statistical models, frequently adopted for describing the probability distribution function (PDF) of ultrasonic backscattered envelopes, have been utilized for tissue characterization. Due to the attenuation increase with ultrasonic frequency, the estimated statistical parameter can be affected by the broad-band attenuation in tissues and distortion of acquired echo signals. Hence, different ultrasonic frequencies and excitation signals were implemented to investigate the attenuation effect on statistical analysis of ultrasonic backscattered signals. Measurements were performed from tissue-mimicking phantoms, which were consisted of gelatin and glass beads with concentrations of 16 and 64 scatterers/mm3, using 3.5 and 7.5 MHz focus transducers. Per each experiment, a phantom was placed between the transducer and tissue-mimicking phantom for creating attenuation. Ultrasound signals were generated by exciting transducers with 1, 3, 5, and 10 cycles sinusoidal signals. The Nakagami statistical model was used to analyze the PDF of ultrasonic backscattered envelopes. This study further indicated that the attenuation could significantly vary the PDF of ultrasonic envelopes especially for the transducer was excited by monocycle sinusoidal signals. As a narrower bandwidth associated with the increase of cycles of tone burst was implemented, the attenuation effect was substantially reduced. The sinusoidal signals of 3 cycles among other excitation signals demonstrated the most appropriate performance to accommodate between attenuation effect and image resolution.

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