FEM MODELING OF PIEZORESISTIVE FORCE SENSOR FOR …...testing cantilever. Investigation results...

FEM MODELING OF PIEZORESISTIVE FORCESENSOR FOR MEDICAL RETRACTOR AND

DESIGN VERIFICATIONSamo Penic, Uros Aljancic, Danilo Vrtacnik, Drago Resnik, Matej Mozek, Matej

Makovec1, Roman Bosnjak2, Slavko Amon

University of Ljubljana, Faculty of Electrical Engineering, Trzaska 25, 1000 Ljubljana,Slovenia

1Department of Surgery, General Hospital Novo Mesto, Smihelska 1, 8000 Novo mesto,Slovenia

2Department of Neurosurgery, University Hospital Center, Zaloska 7, 1000 Ljubljana, Slovenia

[email protected] (Samo Penic)

Abstract

In this paper the numerical modelling of medical retractor for lumbar discectomy is presented.Lumbar discectomy is the most common operative procedure performed by neurosurgeons.During the surgery the retractor is used to alter the position of spinal nerve root in order tooptimize surgical exposure. The force and time of retraction monitoring is the essential stepin the improvement of surgical procedure. The medical retractor was equipped with siliconbased piezoresistive sensors and the prototype was manufactured. The numerical analysis donewith ANSYS Finite element analysis software was used to evaluate the design, characterizeforce sensor used and provides design modifications to improve the retractor usability. Thecharacterization method is explained and the numerical model of the retractor is built usingthe measured values for mechanical and electrical properties. The mechanical properties weremeasured and compared with calculated values. The optimal position of piezoresistive forcesensors is determined by stress distribution in the retractor, where the uniformity of stress andthe stress magnitude was under the consideration. The numerical model also serves as a basisfor extending force measurement in two dimensions. The 2-axis force measurement is requiredto sufficiently monitor the force during the surgery and it is thus essential in the design.

Keywords: force sensor, stress, strain, ANSYS, finite element method, retractor, medicalapplication, piezoresistivity, modeling, silicon

Presenting Author’s BiographySamo Penic was born in 1980 in Celje, Slovenia. In 2006 he received his B.Sc. degree at the Faculty of Electrical Engineering, University of Ljubljanaand became a junior researcher at the Faculty of Electrical Engineering inthe Laboratory for microsensors structures and electronics (LMSE). Heis continuing his postgraduate studies. He is interested in coupled-fieldmodeling of MEMS structures, especially sensors and actuators.

Proc. EUROSIM 2007 (B. Zupančič, R. Karba, S. Blažič) 9-13 Sept. 2007, Ljubljana, Slovenia

ISBN 978-3-901608-32-2 1 Copyright © 2007 EUROSIM / SLOSIM

1 IntroductionLumbar discectomy is the most common operative pro-cedure performed by neurosurgeons. During lumbardiscectomy, a nerve root retractor is used to alter theposition of the involved spinal nerve root in order tooptimize surgical exposure. The rate of success of suchsurgery depends, among others, on the force and timethe force is applied on the nerve. Careful monitoring offorce is thus essential step towards improved surgicalprocedure. In our laboratory we developed and manu-factured force sensor attached to retractor for medicaluse as described by [1] and [2].

In this paper piezoresistive coefficient in longitudinaldirection of sensor chip were determined. In order tocharacterize piezoresistive sensor properties, piezore-sistor was bonded to stainless steel prismatic shapetesting cantilever. Investigation results serve as inputdata of ANSYS finite element analysis software (FEA).The exact material properties of the stainless steel can-tilever, like Young’s modulus was crucial for numericalmodel and were measured independently by two meth-ods – the indentation method and by analysing modalfrequencies. Simple shape of the cantilever allowed an-alytical verification of numerical model.

The geometric model of the actual retractor (D’Errico,MDE, Frittlingen, Germany) was used to verify thestress concentrations at points where the sensor wasmounted in the first prototype, prior to the numeri-cal modelling. On the basis of simulation, the designimprovement is suggested. The retraction during thesurgery is done by applying force in two direction –transverse and longitudinal to the retractor length. Withadditional sensor, the retractor for lumbar discectomycould perform a 2–axis measurement of force applied tothe nerve, which is closer to satisfy surgeon’s require-ments.

Existing designs reported in the literature [3, 4] includesforce sensors at the tip of the retractor where sensor andretractor are in direct contact with the nerve during thesurgery. The proposed design in this article provides anessential advantage, the elimination of the sensor fromthe operative area.

2 Numerical model preparationSilicon has piezoresistive properties thus it is suitablefor indirect force measurement through stress in mate-rial that the force induces. Mechanical stress in siliconchip can be detected as a change in resistance in com-parison with unstressed material. Any force applied onstructure results in mechanical stress in accordance tomaterial Young’s modulus, given by equation

σ = [E]ε, (1)

where σ denotes stress and ε is strain. [E] is theYoung’s modulus and is material depended. The equa-tion 1 is valid in the range of elasticity. If the force is toogreat, the permanent change in material occurs and thelinearity of material behaviour is lost. It is also worth

noting, that stresses and strains are vectors written us-ing a simplified notation by ANSYS, whereas Young’smodulus is a matrix representing a tensor.

The governing equation of the piezoresistive effect isdρ

ρ

= [π]σ, (2)

where [π] represents matrix with stress coefficients ofpiezoresistivity and dρ

ρ relative change in resistivity.

Mechanical properties and geometry of the structuredefine its modal frequencies. For modal analysis aclamped prismatic shaped stainless steel beam wasused, since the analytical relation for its modal fre-quency is known. The Euler-Bernoulli theory was usedto solve the model of clamped bar analytically[5], re-sulting in equation 3.

ωi =β2

i h

l2

√E

12ρv, (3)

In the equation 3, h represents beam height, l its length,E Young’s modulus of the material and ρv its density.The index i denotes the i-th modal frequency. The con-stant βi corresponds to boundary conditions and to themode of vibration. For clamped bar the constant for thefirst modal frequency is indeterminable, for higher fre-quencies the values are given in tabular form (see table1). The values for modal frequencies are close approxi-mates, since the Euler-Bernoulli theory do not take intoaccount the rotational inertia of the cross section andshear deformation.

Tab. 1 Values for constant βi for beam clamped at singleside.

i βi

1 1, 8752 4, 6943 7, 855

Analytical expressions for strain and stress are straight-forward only for basic structures like prismatic bars,cantilevers etc., and are analytically indeterminablefor more complicated structures like cantilevers withnonuniform cross-section. Latter structures are themost commonly occurring in the real world, so anotherapproach is needed for calculating the stress. Numeri-cal analysis provides the answer to the problem. Thereare numerous software packages available on the mar-ket that can perform mechanical and even multiphysicscoupled field analysis. Numerical modelling is usuallyperformed using finite element method (FEM), since itis the method that can be used on various structures dueto its adaptable meshing.

2.1 ANSYS input model

For modeling piezoresistor properties, elements namedSOLID227 were used. These elements have the ca-



pability to model piezoresistive effect in three dimen-sional space. Stress or strain can result in the change ofthe resistivity of the material

[ρ] = [ρ0]([I] + [r]), (4)

where [ρ] is the resistivity of mechanically loaded mate-rial, [ρ0] is resistivity of unloaded material, [I] is iden-tity matrix and [r] is relative change of resistivity [dρ

ρ ].Brackets are used by ANSYS to denote, that the vari-ables are in fact matrices.

Relative change of resistivity (the elements of the ma-trix [r]) is calculated according to equation 2. Equations1 and 2 combined results in another material proper-ties matrix called the piezoresistive strain matrix ([m])that takes into the consideration piezoresistivity matrix[π] and Young’s modulus [E] thus relating r directlywith strain ε.

r = [m]ε (5)

Braces are by ANSYS semantics signaling that r andε are vectors of elements used to build up the cor-responding matrix – for example, vector r = dρ

ρ consists of components that are used to build up the ma-trix with the same name [r].

[r] =

[rx rxy rxz

rxy ry ryz

rxz ryz rz

](6)

where r = [rx ry rz rxy ryz rxy]T

ANSYS uses the relation 5 to solve coupled-field finiteelement problem with with equation 7

[[M ] [0]0 0

]uv

+

[[C] [0][0] [0]

]uv

+ (7)

+[

[K] [0][0] [KV ]

]uv

=

FI

,

where is [KV ] conductivity matrix that includespiezoresistive effect, u is displacement, v is elec-tric potential, [M ] is mass matrix, [C] is damping ma-trix and [K] is stiffness matrix that represents Youngmodulus. Loads are described with vectors F, whichis force and I that represents electric current[6].

2.2 Mesh

The geometry is modelled in 3D space, taking into ac-count the symmetry of the structure where possible.The ANSYS SOLID227 built in elements were usedto model silicon piezoresistors and SOLID92 elementswere used for stainless steel cantilever and retractor.The meshed models are shown on figures 1 and 2.

Fig. 1 Meshed model of piezoresistor chips on stainlesssteel cantilever used to determine coefficients that buildup [π] matrix. Due to the symmetry only half of themodel must actually be solved.

Fig. 2 Meshed model of medical retractor. Stresses inthe retractor are important for piezoresistor placement.

2.3 Material properties

The material properties were largely unknown beforethe modelling and the experiment was matched withnumerical solution with parameter variation until theresults were matched. Since the prismatic shape can-tilever was used, the analytical solutions were useful topredict material properties from measurements.

Silicon Young’s modulus and density were taken fromliterature [7, 8] and are listed in table 2. The piezoresis-tive coefficient in longitudinal direction of the chip di-mensions were determined by experiment and its valueis presented under results.

Testing cantilever used for characterization was madeof the cold rolled Austenitic 14310 stainless steel. ItsYoung’s modulus was determined with the measure-ment of modal frequencies and microindentation tech-nique. The same properties were assumed for medicalretractor.



Tab. 2 Mechanical properties of silicon

Property ValueE11 165.7 GPaE12 63.9 GPaE44 79.6 GPaρv 2330 kg/m3

Fig. 3 Stainless steel cantilever with four piezoresistorsprepared to operate in bridge circuit.

3 Experimental setupPiezoresistors were made on 4-inch, 380µm thick n-type silicon wafer with 〈100〉 orientation and resistiv-ity of 800Ωcm. Sheet resistance of piezoresistor is23kΩ/sq at non uniformity over the wafer better than2.5%.

The characterization of piezoresistors was split into twostages. Firstly the mechanical properties of stainlesssteel cantilever were determined using microindenta-tion technique. The results of multiple measurementsproved to be largely dependent on the location of theindentation, thus an integral method needed to be usedto confirm the measured values.

After the Young modulus for stainless steel cantileverwas determined, the piezoresistors were bonded 1 mmfrom the cantilever support. Cantilever was displacedby known force and change in resistance was measured.In ANSYS the same force was applied and the mea-sured change in resistance was mached with calculatedstress in cantilever. The piezoresistive coefficient wascalculated according to equation 2.

The acquired πL coefficient in longitudinal directionwas used in a model of retractor to allow the calcula-tion of resistance change on load.

The modulus of elasticity of stainless steel cantileverwas determined by two methods. The first was mi-croindetation method [9, 10] which provided scatteredvalues for Young’s modulus. More integral measure-ment method of modal frequencies was used to get ad-ditional results. The cantilever vibration was initiatedwith mechanical deflection and release. The vibrationwas observed by pointing a laser source to the tip of

the cantilever, where it reflected. The reflected ray wasdirected to the photodiode which was connected to theHP4155A semiconductor parameter analyser. The pa-rameter analyser logged the response, which was trans-fered to the computer and the FFT was applied. Themodal frequencies were extracted and compared withsimulated values and analytical values. When the mod-ulus of elasticity was known, the characterization ofbonded piezoresistor chips was possible by loading thecantilever.

Piezoresistors were glued to the retractor and stainlesssteel cantilever with “UHU plus endfest 300” epoxyadhesive that was cured at the highest recommendedtemperature of 180C at which it achieved a bondingstrength of 3000N/cm2. After bonding, the piezore-sistor contact pads and cable interface were connectedwith standard microelectronics golden wire with 25µmdiameter.

Stainless steel cantilever (Figure 3) was used tocharacterize piezoresistive parameter of manufacturedpiezoresistors in longitudinal direction πL. The equa-tion 2 is simplified assuming that the transversalstresses do not contribute to the overall change in re-sistivity.

dρ

ρ= πLσL (8)

The four resistors are setup for bridge measurements,whereas for characterization only one resistor was mea-sured.

The cantilever was loaded with known force and theresponse of the piezoresistor was measured with Semi-conductor Parameter Analyzer HP 4155A. The param-eter analyzer was measuring the voltage on the piezore-sistor while providing the constant current through theresistor. The same response under the same load wasachieved with simulation at while piezoresistivity ma-trix was varied.

Piezoresistor is temperature depended as well as sen-sitive to light. Temperature dependency was mini-mized with usage of two identical piezoresistors in volt-age divider circuit [1]. To mask all incoming light,to protect golden wiring to the substrate and to pro-tect piezoresistor from mechanical and chemical dam-age, both piezoresistors in the retractor prototype de-sign were covered with epoxy casting compound TRA-CAST 3103. Used epoxy compound is non-toxic andmedical compatible.

Glue bonding and epoxy casting was not used in nu-merical model, since its influence was estimated to benegligible. Some additional simplifications were madein preparation of the model, since the model was toocomplex to manually enter it into the simulation soft-ware. The shape of the model corresponds to the actualretractor, but there were some minor differences mostlyat the corners. Namely, retractor smooth corners werereplaced with model sharp edges. The influence of thissimplification was estimated to be of no importance far



Fig. 4 Depth–load diagram determined by the indenta-tion method. (From the slopes of the curves and startingand ending load point the Young’s modulus is calcu-lated by the method described in [9].)

from the physical borders where all the measurementswere done.

With numerical model the optimal position of thepiezoresistors was determined, taking into account sev-eral requirements, such as high sensitivity to the stim-ulus and high uniformity of stress on the piezoresistorsurface. The final location of sensor was also condi-tioned with surgeon requirements such as the fact thatit should not block the view in the operative field.

4 Results and discussionWith indentation method the Young’s modulus was de-termined. The measured Young’s modulus for stainlesssteel cantilever was averaged on the basis of 8 measure-ments as E = 167, 56 GPa, whereas the maximum andminimum values were scattered over the range of 12%of average value. Difference in measurements were as-signed to non-uniform surface of stainless steel can-tilever.

Using the Equation 3 and Young’s modulus determinedby microindentation method the same value was usedas input for the ANSYS model and modal analysis wasdone. In Table 3, there is a list of modal frequenciesacquired by measurement, numerical model and ana-lytical solution. Due to low sampling rate of parameteranalyser and due to the fast decay of higher modal fre-quencies, only two modal frequencies were extractedfrom measurements using FFT.

Tab. 3 Modal frequencies of stainless steel cantilever inlongitudinal mode

i Measurement Simulation Analytical solution1 75, 68 Hz 80, 91 Hz 79, 71 Hz2 492, 8 Hz 507, 92 Hz 496, 23 Hz

Values acquired by numerical model are higher thanmeasured values, but still confirm the measured

Fig. 5 Stresses in longitudinal (x) direction in loadedretractor.

Young’s modulus. The Euler–Bernoulli theory pro-vides good agreement to measured frequency at givenYoung’s modulus. We have thus confirmed the inden-tation method measurements of Young’s modulus withanalytical and numerical tools.

In characterization of piezoresitors, the piezoresistiv-ity coefficient πL was calculated from resistance mea-surements. Resistance was measured with loaded andunloaded cantilever. Load was matched in ANSYSmodel and the average stresses on resistors were read-out. From the stress in the resistor and the resistancechange, the coefficient πL was calculated. All measure-ments were done at 23 C. The results are listed in table4.

Tab. 4 Measured resistances under various loads on can-tilever beam and average stresses on piezoresistors ac-tive area.

F [mN] Rx[kΩ] σx[MPa]0 8, 1637 078 8, 1822 6441 8, 2587 31696 8, 2805 371010 8, 3847 691138 8, 4116 781452 8, 4725 1001707 8, 5350 117

Using the data from table 4 the piezoresistive coeffi-cient πL was calculated to be 38, 3 ·10−11Pa−1 and it’svalue is in good agreement with published results [11].The π coefficients are important as they influence thefinal sensitivity of the device. The cantilever character-ization of sensor is now superseded with simulation ofmedical retractor. Calculated stresses with color scaleare shown on figure 5. Longitudinal stress is strongestat the retractor support – at the point where the retrac-tor is hand held. The point of support is not uniquelydefined and it strongly varies with different fingers po-sition during the retractor usage. Another interesting



(a)

(b)

Fig. 6 Two prototype retractor for force measurement.Piezoresistors are covered with black epoxy cast. (a)Sensors bonded on back side. (b) Sensors bonded onfront side.

area, where the stresses are of similar magnitude, is thesection where the retractor is curved in S-shape. Thecurvature acts as a partial support for the long retractorarm of the retractor and it is thus the region of increasedstress.

The uniformity of the stress is also of importance, sincethe resistors bonded on the retractor will always havesome variance in position. Thus small deviation fromdesignated position should have no major influence onthe sensor performance.

5 ConclusionSimulation and mechanical characterization of stainlesssteel cantilever was shown. In combination with numer-ical analysis software the longitudinal piezoresistive co-efficient πL was determined. Results from cantileveranalysis were then applied in the case of retractor. Us-ing ANSYS simulations it was determined that retractorresponse is insensitive to piezoresistors position varia-tion because of good uniformity of stress distributionon retractor arm.

The final prototype retractor was built on the basis ofpractical aspects and surgeon requirements. The back

side of the retractor (Figure 6) was used for the first pro-totype. Later on this was discarded, because the sensorblocked the view into the operative field. Therefore thesensors were mounted at the front side. In addition thesensor was still mounted on an area with large stress.Sensitivity was thus maximized by optimal sensor po-sition.

The proposed method of retraction force measurementhas an advantage in comparison with published designs,since it doesn’t involve force measurement in operativefield. Removing the sensor away from the biologicalsystems provides protection from interference, such aselectrical voltages, that could potentially result in neu-ral response.

The numerical simulation provided invaluable results interms of design verification and design improvement.Numerical results enable insight into mechanical stressdistribution of loaded retractor and represent the basisfor improvement of design.

The retraction is not applied only in one direction, butis usually combined or it can shift from one directionto another. Additional sensors on such a retractor willprovide further improvements in dual-axis force mea-surements. With additional software the influence oforthogonal stress components in cantilever, which areresult of forces acting in different directions, could beevaluated resulting in total force vector acting on anerve.

6 AcknowledgmentWe would like to acknowledge prof. Peter Panjan fromIJS, Slovenia for providing the microindentation mea-surements.

7 References[1] Uros Aljancic, M. Makovec, D. Vrtacnik,

D. Resnik, M. Mozek, R. Bosnjak, and S. Amon.Piezoresistor as a retraction force sensor. 41th In-ternational Conference on Microelectronics, De-vices and Materials and the Workshop on GreenElectronics, pages 263–268, 2005.

[2] U. Aljancic, D. Resnik, D. Vrtacnik, M. Mozek,and S. Amon. Retraction force measurement withsilicon piezoresistor. 29. International ConventionMIPRO 2006, pages 245–251, 2006.

[3] H. Matsui, H. Kitagawa, Y. Kawaguchi, andH. Tsuji. Physiologic changes of nerve root duringposterior lumbar discectomy. Spine, 20(6):654–659, 1995.

[4] C. Feltes et. al. Effects of nerve root retractionin lumbar discectomy. Neurosurg Focus, 13(2),2002.

[5] Giancarlo Genta. Vibration of structures and ma-chines. Springer Verlag, New York, 2. edition,1995.

[6] Inc. Ansys. ANSYS, Inc. Theory reference. Ansys,Inc., 2005.

[7] J.J. Wortman and R.A. Evans. Young’s modulus,shear modulus and poisson’s ratio in silicon and



germanium. J. of applied physics, 36(1):153–156,1965.

[8] James F. Shackelford and William Alexander.CRC Materials Science and Engineering Hand-book. CRC Press, 3. edition, 2001.

[9] Rashid K. Abu Al-Rub. Prediction of microand nanoindentation size effect from conical orpyramidal indentation. Mechanics of Materials,(39):787–802, 2007.

[10] Dejun Ma, Kewei Xu, Jiawen He, and Jian Lu.Evaluation of the mechanical properties of thinmetal films. Surface & Coatings Technology,pages 128–132, 1999.

[11] Y. Kanda. A graphical representation of thepiezoresistance coefficients in silicon. IEEETransactions on Electron Devices, 29(1):64–70,1982.



FEM MODELING OF PIEZORESISTIVE FORCE SENSOR FOR …...testing cantilever. Investigation results...

Documents

Transcript of FEM MODELING OF PIEZORESISTIVE FORCE SENSOR FOR …...testing cantilever. Investigation results...