基于聲信號(hào)處理的骨銑削狀態(tài)監(jiān)測(cè)

基于聲信號(hào)處理的骨銑削狀態(tài)監(jiān)測(cè)

代煜1，雪原2，張建勛1

(1.南開大學(xué)機(jī)器人與信息自動(dòng)化研究所，天津300071； 2.天津醫(yī)科大學(xué)總醫(yī)院骨科，天津300052)

摘要：考慮聲信號(hào)能提供關(guān)于切削刀具及組織接觸狀態(tài)信息，通過采集、分析在椎板切除術(shù)中產(chǎn)生的聲信號(hào)實(shí)現(xiàn)銑削狀態(tài)監(jiān)測(cè)。建立微分方程描述椎板受切削力作用的受迫振動(dòng)，證明振幅隨骨厚度減少而增大。利用離散小波變換從采集的聲壓信號(hào)中提取主軸頻率整數(shù)次諧波分量，通過計(jì)算特殊尺度的小波能量積判斷銑削狀態(tài)。用所提狀態(tài)監(jiān)測(cè)方法對(duì)豬脊柱進(jìn)行銑削實(shí)驗(yàn)，并獲得驗(yàn)證。結(jié)果表明，椎板將要被穿透時(shí)小波能量積會(huì)顯著增大。

關(guān)鍵詞：手術(shù)機(jī)器人；銑削狀態(tài)監(jiān)測(cè)；聲信號(hào)處理；小波變換

中圖分類號(hào):TP242.3文獻(xiàn)標(biāo)志碼：A

Bone milling condition monitoring based on sound signal processing

DAIYu1,XUEYuan2,ZHANGJian-xun1(1. Institute of Robotics and Automatic Information System, Nankai University, Tianjin 300071, China；2. Orthopedics, Tianjin Medical University General Hospital, Tianjin 300052, China)

Abstract:In consideration of that the sound can provide useful informations about tool-tissue contact, the condition monitoring was realized by acquiring and analyzing the sound signal during laminectomy surgery. A differential equation was presented to describe the vertebral lamina vibration excited by the cutting force, and it is proved that the vibration amplitude will increase as the thickness of the bone decreases. Discrete wavelet transform was performed to extract the harmonic components whose frequencies are integer multiples of spindle frequency from the sound pressure signal, the products of wavelet energy at some special scales were calculated to judge the milling status. The proposed condition monitoring method was experimentally verified through the milling operation in porcine spines, and the results indicate that the product of wavelet energy will increase significantly when the vertebral lamina is going to be penetrated.

Key words:surgical robot; milling condition monitoring; sound signal processing; wavelet transform

骨外科手術(shù)中醫(yī)生常通過輸出可控機(jī)械動(dòng)能驅(qū)動(dòng)銑刀、鉆頭等器械暴露或切除病灶。對(duì)傳統(tǒng)的人工手術(shù)方式而言，切削骨組織技術(shù)參數(shù)(包括進(jìn)給量、切削深度及速度等)完全由醫(yī)生自行掌握，因此靈活利用動(dòng)力工具須靠醫(yī)生長(zhǎng)期體會(huì)與經(jīng)驗(yàn)積累。較多骨外科手術(shù)工作空間較狹小，不同患者個(gè)體有一定病理、解剖變異，高速旋轉(zhuǎn)的刀具較易碰到重要組織造成無法修復(fù)的損傷。手術(shù)機(jī)器人為解決該問題提供了可能。通過安裝在機(jī)器人手臂的傳感器檢測(cè)、估計(jì)切削刀具與骨組織相對(duì)接觸位置變化，若遇危險(xiǎn)狀態(tài)可及時(shí)改變切削技術(shù)參數(shù)，從而避免對(duì)正常組織的損傷。已用狀態(tài)監(jiān)測(cè)方法見表1。手術(shù)動(dòng)力工具主要靠可更換的多種刀具實(shí)現(xiàn)切削功能。刀具在進(jìn)給過程中的受力變化可直接反映與組織的相互作用狀態(tài)[1]。由表1可見，諸多研究選用直接或間接檢測(cè)切削力、力矩方法。該方法優(yōu)勢(shì)在于力、力矩信號(hào)易采集，響應(yīng)速度快。而傳感器不能安裝在高速旋轉(zhuǎn)的刀具上，實(shí)際安裝位置距離刀具與骨組織接觸點(diǎn)較遠(yuǎn)，會(huì)降低信號(hào)的信噪比。文獻(xiàn)[2-3]提出利用骨振動(dòng)信號(hào)、骨組織電阻抗變化實(shí)現(xiàn)鉆頭穿透皮質(zhì)骨辨識(shí)，并分別進(jìn)行活體、離體動(dòng)物實(shí)驗(yàn)。結(jié)果表明，辨識(shí)準(zhǔn)確率均在90%以上。

基于聲信號(hào)處理的特征提取已成重要的機(jī)械故障診斷方法[4]，但未在骨外科手術(shù)中應(yīng)用。經(jīng)驗(yàn)豐富的外科醫(yī)生可通過仔細(xì)辨別刀具切削骨組織時(shí)的聲音判斷手術(shù)過程及狀態(tài)，說明切削聲音信號(hào)可作為識(shí)別手術(shù)過程、狀態(tài)的監(jiān)測(cè)信號(hào)。較表1其它狀態(tài)監(jiān)測(cè)方法具有的優(yōu)勢(shì)為：聲信號(hào)獲取較容易，所用傳感器及數(shù)據(jù)采集設(shè)備價(jià)格較低，傳感器安裝簡(jiǎn)單，不改動(dòng)機(jī)器人手臂且定位精度要求較低；聲信號(hào)采集對(duì)手術(shù)過程無影響；缺點(diǎn)在于手術(shù)環(huán)境存在諸多聲源，使大量噪聲混雜在采集的聲信號(hào)中，須對(duì)聲信號(hào)進(jìn)行適當(dāng)處理。

本文以椎板切除手術(shù)為例，通過檢測(cè)、分析銑削骨組織過程中產(chǎn)生的聲壓信號(hào)，分辨椎板即將穿透前的臨界狀態(tài)，用于手術(shù)機(jī)器人中以提高安全性。

表1　骨外科手術(shù)狀態(tài)監(jiān)測(cè)方法

1骨銑削過程中聲信號(hào)采集

手術(shù)動(dòng)力工具作為機(jī)械動(dòng)能的輸出設(shè)備，也是振動(dòng)激勵(lì)源。椎體受切削力影響產(chǎn)生振動(dòng)，并引起周圍空氣振動(dòng)且通過縱向波傳播，最終被麥克風(fēng)接受。因此本文采用圖1方法測(cè)量手術(shù)過程中產(chǎn)生的聲壓信號(hào)。選符合1類聲級(jí)計(jì)標(biāo)準(zhǔn)的自由場(chǎng)麥克風(fēng)GRAS-46BE及高精度聲壓信號(hào)采集模塊USB-4431 (均為美國國家儀器公司)，其具有最高102.4 kS/s同步采樣率、24位分辨率，完全能滿足骨銑削噪聲分析要求。

圖1　骨切削過程中聲壓測(cè)量方法 Fig.1 Measurement method of sound pressure during bone cutting

2骨受迫振動(dòng)建模

切削振動(dòng)中含自由、受迫及自激振動(dòng)特征，本文僅研究受迫振動(dòng)，即骨振動(dòng)信號(hào)為手術(shù)動(dòng)力工具主軸頻率的整數(shù)次諧波。考慮椎板為脊髓腔頂部骨組織的某部份，具有中部懸空且兩端與椎體連接的結(jié)構(gòu)特點(diǎn)，因此將其簡(jiǎn)化為等截面直梁，兩端固定，并在OXY平面內(nèi)作橫向振動(dòng)，見圖2。

圖2　椎板簡(jiǎn)化歐拉-伯努利梁模型及其橫截面 Fig.2 A simplified Euler-Bernoulli beam model of vertebral lamina and its cross section

為便于計(jì)算，將手術(shù)中球形銑刀作用于椎板的力視為梁中點(diǎn)集中力。設(shè)梁密度為r，長(zhǎng)度為l，橫截面積為A，材料彈性模量為E，截面對(duì)中性軸慣性矩為I，手術(shù)動(dòng)力工具主軸轉(zhuǎn)動(dòng)角頻率為w。據(jù)歐拉-伯努利梁模型可寫出橫向振動(dòng)微分方程為

(1)

由于銑刀安裝偏心及機(jī)構(gòu)不平衡影響，切削力中應(yīng)含變化分量，為Fysin(ωt)。恒力僅使梁產(chǎn)生固定彎曲變形，因此僅需考慮梁受隨時(shí)間變化的力Fysin(ωt)影響的振動(dòng)。該方程的解為

(2)

式中：ωn為梁的固有頻率，即

(3)

對(duì)寬b厚h的矩形截面(圖2(b))，式(3)可簡(jiǎn)化為

(4)

3銑削力對(duì)脊柱振動(dòng)影響理論分析

由人體脊柱模型測(cè)得24塊椎骨椎板長(zhǎng)度l的平均值為40 mm，厚度為h的平均值為6 mm，據(jù)皮質(zhì)骨彈性模量E= 3.3 GPa及密度ρ=1 800 kg/m3[24]，由式(4)得固有頻率ωn=6.03×105(2n+1)2hrad/s。椎板被銑削的越薄(相當(dāng)于h、A越小)時(shí)，梁的固有頻率ωn也減小(h=1時(shí)ωn=6.03×102(2n+1)2rad/s)，而激勵(lì)力Fysin(ωt)的頻率較高(銑削轉(zhuǎn)速一般為幾萬轉(zhuǎn)/分)，故式(2)可簡(jiǎn)化為

(5)

由式(5)可見，椎板變薄梁各點(diǎn)振幅均提高；椎板被穿透瞬間，因骨組織快速回彈使振幅達(dá)最大值。銑削力中含主軸頻率的高次諧波分量時(shí)，高次諧波幅度同樣會(huì)隨椎板厚度減小而增大，使麥克風(fēng)獲得同頻率聲壓信號(hào)幅度變大。

4聲壓信號(hào)處理

(6)

聲壓信號(hào)s(t)在尺度因子為a、時(shí)移因子為b時(shí)的連續(xù)小波變換可表示為

式中：a,b，t均為連續(xù)變量，a>0；ψ*(·)為復(fù)共軛。

考慮連續(xù)小波變換計(jì)算量較大，利用離散小波分解算法，即小波變換相當(dāng)于以高、低通濾波器對(duì)待分析信號(hào)進(jìn)行數(shù)字濾波及降采樣運(yùn)算。令s(n)表示連續(xù)信號(hào)s(t)的數(shù)字信號(hào)，Ws(i,n)表示第i層分解小波變換系數(shù)，則能量可表示為

(8)

小波系數(shù)能量可反映信號(hào)s(n)的能量沿尺度方向分布情況。據(jù)式(5)結(jié)果，僅需研究聲壓信號(hào)中主軸頻率的整數(shù)次諧波分量，此分量必落在某一層小波變換系數(shù)中，設(shè)一～四次諧波分別落在第i1～i4層中，則定義信號(hào)的小波能量積為

(9)

能量大小反映出骨骼的振動(dòng)狀態(tài)，若此幾層的能量值較大則說明諧波幅度較大。據(jù)式(5)，當(dāng)椎板被銑削的越薄時(shí)，由于椎板振幅提升將導(dǎo)致式(9)的值變大，因此小波能量積可作為判斷椎板被銑薄直至穿透的依據(jù)。

5實(shí)驗(yàn)驗(yàn)證

取鮮豬脊骨沿左側(cè)椎弓跟內(nèi)側(cè)面矢狀位切開，保留與脊柱相連的部分肌肉，手持動(dòng)力工具銑削椎板，銑削中盡量保持施力均衡，用圖1方法利用麥克風(fēng)采集銑削中聲壓信號(hào)。手術(shù)動(dòng)力工具轉(zhuǎn)速設(shè)為30 000 r/min(相當(dāng)于角頻率ω=1 000π rad/s)，并安裝外徑為5 mm的球形銑刀。聲壓信號(hào)采集模塊采樣頻率設(shè)為10 000 Hz，選Db5小波對(duì)聲壓信號(hào)進(jìn)行4層小波分解，見圖3。據(jù)轉(zhuǎn)速計(jì)算出轉(zhuǎn)動(dòng)頻率一次諧波位于第四層小波分解的高頻系數(shù)上，二次諧波位于第三層，三、四次諧波位于第二層。通過小波變換，亦可濾除其它頻帶的噪聲。

對(duì)骨銑削中采集的聲壓信號(hào)截取空轉(zhuǎn)、銑刀剛接觸椎板、接近穿透及穿透四個(gè)典型階段數(shù)據(jù)計(jì)算快速傅里葉變換(FFT)，采樣時(shí)長(zhǎng)0.5 s，四段信號(hào)頻譜見圖4。由圖4看出，手術(shù)動(dòng)力工具銑削椎板時(shí)，轉(zhuǎn)動(dòng)頻率一～四次諧波幅度均發(fā)生改變，即椎板被切削得越薄時(shí)四次諧波幅度有不同程度增大。值得注意的是，圖4(d)中穿透階段小波能量積變大，并非因主軸頻率整數(shù)次諧波分量幅值變大所致，而因在穿透瞬間切削力消失導(dǎo)致骨組織突然回彈，在聲壓信號(hào)上表現(xiàn)為尖脈沖。聲壓信號(hào)中亦含高、低頻噪聲，通過選特定小波分析尺度可一定程度上減小噪聲對(duì)狀態(tài)監(jiān)測(cè)影響。

圖3　四尺度小波分解樹 Fig.3 Four-scale wavelet decomposition tree

圖4　骨銑削過程中聲壓信號(hào)頻譜 Fig.4 Frequency spectrum of recorded sound pressure signal in bone milling process

據(jù)式(9)與圖3，本實(shí)驗(yàn)取第二～四層小波變換系數(shù)能量乘積。椎板穿透過程中小波能量積的變化曲線見圖5，圖中極大值點(diǎn)對(duì)應(yīng)椎板穿透時(shí)刻，與式(5)分析結(jié)果一致。在兩根脊椎上分別進(jìn)行5次銑削實(shí)驗(yàn)，對(duì)各次的聲信號(hào)均用本文方法進(jìn)行分析，結(jié)果見表2。表2數(shù)據(jù)為10次銑削均值及方差?？梢?，椎板將被穿透時(shí)小波能量積顯著增大。

用Matlab軟件(2012a)的小波工具箱實(shí)現(xiàn)聲壓信號(hào)小波能量積的計(jì)算，所用計(jì)算機(jī)硬件配置為主頻3.3 GHz的Xeon 四核CPU，16 G內(nèi)存，操作系統(tǒng)為64位Windows 8, 處理0.5 s聲壓信號(hào)平均耗時(shí)0.12 s，能滿足對(duì)骨組織銑削過程實(shí)時(shí)監(jiān)控需要。

圖5　椎板穿透過程中的小波能量積 Fig.5 Product of wavelet energy during vertebral lamina penetration

狀態(tài)小波能量積空轉(zhuǎn)開始銑削穿透前2s穿透前1s穿透4.68±0.176.21±0.487.11±0.528.12±0.3911.94±1.81

6結(jié)論

利用所提基于聲壓信號(hào)處理的骨銑削狀態(tài)監(jiān)測(cè)方法，考慮銑削力對(duì)脊柱振動(dòng)影響，用歐拉-伯努利梁的受迫振動(dòng)方程分析振幅變化。結(jié)論如下：

(1)椎板振幅隨其變薄而增大?？捎秒x散小波變換對(duì)聲壓信號(hào)進(jìn)行多層分解，通過計(jì)算小波能量積實(shí)現(xiàn)銑削狀態(tài)識(shí)別。

(2)小波變換頻帶分析特點(diǎn)能克服手術(shù)動(dòng)力工具受切削力影響轉(zhuǎn)速發(fā)生的小幅度改變影響。利用快速傅里葉變換分析時(shí)需搜索的局部極大值位置，計(jì)算復(fù)雜，且聲壓信號(hào)干擾較大，易出現(xiàn)誤判。

(3)本文方法簡(jiǎn)便有效，能提高骨外科手術(shù)機(jī)器人操作的安全性。

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