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| Title: | 應用Biot理論於海綿骨之相速度與聲響性質分析 |
| Other Titles: | Determination of phase velocity and acoustic characteristics in cancellous bone by Biot theory |
| Authors: | 顧庭碩;Ku, Ting-shuo |
| Contributors: | 淡江大學機械與機電工程學系碩士班
蔡慧駿;Tsay, Huoy-shyi |
| Keywords: | 海綿骨;相速度;脈衝回波模擬;Cancellous Bone;Phase Velocity;Pulse Echo Simulation |
| Date: | 2009 |
| Issue Date: | 2010-01-11 06:37:28 (UTC+8) |
| Abstract: | 本文應用Biot多孔彈性動態理論以脈衝回波法分析頻域與時域之海綿骨相速度。研究中首先進行Biot多孔彈性材料動態統御方程組之拉普拉斯轉換，再配合脈衝回波量測之邊界條件，及拉普拉斯轉換因子與角頻率的關係(s=iω)，求得海綿骨頻域之相速度解析解與海綿骨表面位移函數。時域之海綿骨相速度分析則利用海綿骨表面位移頻域函數搭配平頂函數窗之濾波函數，於時域中由波傳時間差計算其相速度。另應用無因次化分析，探討各個無因次化參數於快速波與慢速波無因次相速度的影響。
應用海綿骨之相速度理論解，可探討海綿骨受骨骼材料性質之影響。經與超音波實驗數據比較驗證，本文由理論解預估之相速度結果和趨勢與實驗數據完全吻合。另應用脈衝音壓回波位移頻率響應模擬超音波脈衝回波反應所計算之快速波與慢速波相速度也與解析值完全吻合。本文由海綿骨材料參數變異於脈衝回波之影響分析方面發現固體密度ρs、材料固體架構體積模數Kb與剪力模數N等影響到快速波之相速度；流體體積模數Kf影響到慢速波之相速度；而孔洞係數φ及結構因子α∞對快速波與慢速波皆產生影響；惟有固體體積模數Ks對相速度之影響較不顯著。
另本文由無因次參數變異分析也發現，在無因次快速波相速度部份，無因次彈性係數R*在低頻區影響最大，而P*在高頻區影響最大；此外在無因次慢速波部份則以R*值影響較大。另一方面無因次固體有效密度主要影響快速波相速度；而增加液體有效密度對中頻以後之快速波相速度卻無影響，但會降低慢速波相速度之起始值；另耦合有效密度 值增高，對應之相速度也隨之增高。至於增高無因次消散係數 則會使相速度曲線往高頻移動但不改變曲線形狀。
In this study, Biot’s poroelastic theory is used to derive the pulse echo responses and phase velocities of fast and slow waves of cancellous bones. First, Biot’s equations were transformed to Laplace domain. By specifying the boundary conditions for the pulse echo simulation and the relation between the Laplace transform parameter and the angular frequency(s=iω), the theoretical frequency response functions of phase velocities and the displacement of the driving surface of the cancellous bone were obtained. In time domain, phase velocities of cancellous bone were analyzed using the displacement frequency response function obtained and flat top windows, and were calculated from the rate at which the phase of the wave propagates. In the end of this study, the influences of dimensionless material parameters on the dimensionless phase velocities of fast and slow waves were discussed.
Using the phase velocity results derived the influences of bone properties on the phase velocities were numerically analyzed. The predicted results were validated by ultrasonic experimental results and a good agreement was observed. The phase velocities, which were calculated from the phase propagation rate, also agreed well with the results derived. After the influence analyses of bone properties on the phase velocities, it was found that the density the solid, the bulk modulus of the frame, the shear modulus of the frame affect the phase velocity of the fast wave. The bulk modulus the fluid affect the phase velocity of the slow wave. The porosity and tortuosity of the bone affect both waves. The only one parameter that has minor effects is the bulk modulus of the solid.
After the analyses of the dimensionless bone properties on the phase velocities, it was found that the dimensionless Biot’s coefficients R* and P* have major effects on the phase velocity of the fast wave in low frequency and high frequency regions, respectively. Moreover, the dimensionless Biot’s coefficient R* affect the phase velocity of the slow wave. Furthermore, the dimensionless total effective mass density of the solid affects the phase velocity of the fast wave. The increase of the dimensionless total effective mass density of the fluid has no effect on the phase velocity of the fast wave above the low frequency region, but will decrease the initial value of the phase velocity of the slow wave. Increasing the value of the coupling mass density will also increase the value of the phase velocities accordingly. Nevertheless, enlarging the value of the dimensionless dissipation coefficient will move the phase velocity curve toward the high frequency side but makes no change to the shape of the curve. |
| Appears in Collections: | [機械與機電工程學系暨研究所] 學位論文
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