A novel elastometer for soft tissue

Transcription

1 Computational Methods and Experiments in Material Characterisation II 111 A novel elastometer for soft tissue S. M. Harrison 1, M. B. Bush 1 & P. Petros 1,2 1 University of Western Australia 2 Royal Perth Hospital Abstract A novel device has been designed to allow a surgeon to determine the medium strain (5-25%) compressive properties of highly extensible soft tissue during a surgical procedure. The motivation for the instrument is the need for accurate knowledge of the elastic properties of vaginal tissue in vivo during corrective surgery for incontinence in women. Studies have shown that a surgical technique that adjusts the elastic nature of vaginal tissue can reduce urge and stress incontinence symptoms. The success of the surgical technique would be greatly enhanced by the introduction of an objective measure of the stiffness of vaginal tissue. The compressive deformation is achieved by folding and pinching (indenting) the tissue between two circular cylinders. The applied load and indentation depth are used to estimate the elastic properties of the sampled tissue. A linear material model has been developed and tested against commercially available elastomers. The limits of application of the linear material model were determined using FEA and results from the experimental testing. A basic nonlinear model is also presented that can determine the Neo-Hookean constant of the material. The simple algorithms developed allow immediate inversion of measurements to give elastic properties, thereby permitting multiple readings to be made during a surgical procedure, an outcome that would not be possible if FEA or similar numerical methods were needed for interpretation of the readings. Experimental and numerical results are compared to the analytical models and a discussion of initial design ideas is presented. The device is shown to yield elastic modulus of test materials with an error of less than 10%. Keywords: soft tissue elastometer, large strain, FEA, in-vivo. 1 Introduction The knowledge of a measure of the elastic nature of particular human tissue structures has significant value to many areas of medicine. In particular some

2 112 Computational Methods and Experiments in Material Characterisation II tissue structures fulfil structural roles that depend on their elastic response. Failure of this role may necessitate surgical correction - quantitative measurement of the elastic properties of the tissue could enhance the success rates of such procedures. Incontinence is a problem experienced by up to half of the female population [1], depending on age. Symptoms include leakage due to stress such as sneezing or coughing (stress incontinence) and increased frequency of the need to empty (urge incontinence). Treatments range from symptom orientated solutions, such as absorption pads, to preventative measures such as muscle training exercises and surgery. The latter is the most successful [2], but may be excessive for some patients. Petros and Ulmsten proposed the Integral Theory of Incontinence [3], which suggests that the tensile state of the vaginal hammock is a deciding factor in urge and stress incontinence. Fig 1 shows how the urethra connects to the pubococcygeus muscle (PCM) via the vaginal hammock. In the case of a stress situation (e.g. a cough or sneeze) the PCM pulls against the levator plate (LP) and the longitudinal muscle of the anus (LMA) to kink the urethra, while other structures act to reduce the diameter of the urethra [4]. If the vaginal tissue is too lax then excessive extension of this structure will limit the extent of the kink that can be applied to the urethra. Significant laxity can be caused by trauma (such as childbirth) or ageing, leading to leakage. An incorrect magnitude of tension in the vaginal hammock can also displace the bladder. This results in pressure on the nerve bundles that would normally only be under pressure when the bladder is full. Subsequently the brain is prematurely signalled of the need to empty. This is an example of an urge incontinence symptom. Corrective surgery using this model is successful, but could be improved by a device that measures the elastic properties of the vaginal hammock in the surgical environment. Elastometers suitable for application to soft tissue have been under development for the last thirty years. In general a deformation is applied to the tissue and a measure of elasticity estimated by interpreting the load-displacement relationship. Indentation by a spherical indentor has been the more prevalent type of deformation employed. Hayes popular boundary value solution [5] was utilised by Lyyras [6] in a novel arthroscopic device that removes some of the uncertainty of indentation depth. Toyras [7] employed ultrasonic thickness measurement to further enhance results. Testing site conditions may prohibit the use of indentation for the accurate determination of the mechanical properties of soft tissue. In this case other methods must be developed, taking into account accessibility, material geometries and current technologies. Instruments employing pipette aspiration [8], balloon inflation [9] and sonic methods [10] have been developed for various applications. All methods produce a complex deformation that makes interpretation of the force-displacement relationship an equally complex task. In this study we propose a localised indentation method based on the concept of pinching of skin between the thumb and forefinger. Two effectively rigid cylinders are employed to fold and then compress (indent) the test tissue. The required load to indent the tissue to a certain depth gives a measure of the

3 Computational Methods and Experiments in Material Characterisation II 113 mechanical response of the tissue. This deformation has the advantage of isolating the test area, or pinch zone (Fig 2), from surrounding structures and eliminates the need for complex spatial imaging. Output from the instrument can be processed immediately, allowing for multiple readings to be made during a surgical procedure. (a) (b) Figure 1: Anatomy of the female pelvic floor relevant to stress incontinence. The pubococcygeus muscle (PCM) attaches to the urethra via the vaginal hammock (VH). During emptying the urethra is relatively straight (a). Under stress (b) the PCM pulls against the levator plate (LP) and the longitudinal muscle of the anus to kink the urethra as part of the closing mechanism. An incorrect stiffness of the vaginal tissue may lead in incomplete closure and hence incontinence. A linear elastic model has been developed to determine either the initial (zero strain) elastic modulus or a hyperelastic material constant. To date, the model has been used to estimate the elastic properties of nonlinear polymer materials. Finite Element Analysis and experimental observation have been used to determine the limits of application of these models. The focus of this study was to design and test a prototype of the device that resembles an instrument that could be used in surgery 2 Analysis The deformation in the pinch zone (Fig 2) is modelled as a symmetric indentation by a rigid cylinder of finite length. A known solution to the

4 114 Computational Methods and Experiments in Material Characterisation II analogous planar problem (cylinder of infinite length) is corrected to allow for the end effects caused by the finite length of the indentor. Alblas and Kuipers provided a closed form of the load exerted during planar indentation by a rigid cylinder on a thin strip [11]: c 2 3 b b b E c = , (1) 2 R c c c 2( 1 υ ) b P C 2 where P C is the applied load, R is the radius of the indentor, b is the thickness of the sample, E is the elastic modulus, υ is the Poisson ratio and c is the contact width, which is calculated from the indentation depth at the centre of the indentor, v 0 : c = (0.170b) 2 2 (0.029b 2 v 0 R) 0.170b. (2) The end effects are estimated by reference to the analogous case of indentation by a rigid rectangular punch. Solutions for the case of a punch of finite width and the case of an infinite punch (uniaxial compression) are both available. It is postulated that the necessary correction to planar uniaxial compression that accounts for the edge effects associated with a finite punch is similar to the correction required to adjust between the cases of indentation by an infinite cylinder and indentation by a cylinder of finite length. Alblas and Kuipers provided a closed form representation of the forcedisplacement relationship for planar rectangular indentation of an incompressible material [12]: P FLAT v b 4E = 1 + (3) b 4 C 3 In this case the applied load is P FLAT, and C is the half width of the indentor. Planar compression is similar to uniaxial compression, except that the inplane strain normal to the direction of the indentation is zero: P v0 4 = E U b 3. (4) The end effect correction to (1) is estimated by the ratio of P FLAT to P U, resulting in the indentation force, F: PFLAT F = PC. (5) P Studies have shown that it is possible to determine a nonlinear material parameter from the instantaneous elastic modulus E for any load-displacement U

5 Computational Methods and Experiments in Material Characterisation II 115 data set taken from a non-linear elastic material. The relationship appears to be adequately represented by an exponential function: ε = (Ae Bv 0 / b + D) ln 1 v 0, (6) b where ε is the effective true strain and v 0 /b is the nominal strain. The variables A, B and D have been determined from Finite Element analysis and appear to be representative of the reaction of all materials tested so far. Assuming a Neo-Hookean hyperelastic model, the single nonlinear material parameter, C 10, may be estimated by: C 10 = E 2(2e 2ε + e ε ). (7) If the Neo-Hookean model adequately represents the stress-strain behaviour of the test material in the appropriate strain range then this is more informative measure of elastic response. 3 Materials Two commercially available elastomers were employed to model soft tissue. Hyperelastic (Mooney-Rivlin) material models were fitted to uniaxial test data (tensile and compressive, N=25). Samples were cut from the sheeting using a punch. The samples were of different stiffness and thickness to allow testing of the generality of the theoretical model. Sample 1 was 1.6 mm thick and was modelled with Mooney Rivlin constants C 10 = 1.2 MPa, C 01 = 0 MPa. Similarly Sample 2 was 3 mm thick, with C 10 = MPa, C 01 = MPa. 4 Method A prototype elastometer was designed and constructed (Fig 2). Two scissoring arms pivoted on a low friction bearing were driven by a stepper motor. The prototype allows for various cylinder sizes to be employed. Strain gauges were attached near the bearing (at the point of maximum flexure) to capture the deflection of the arms with the greatest sensitivity. Displacement of the contacts was determined by the speed of the stepper motor, corrected for the flexure of the arms, and verified by a large travel (±25mm or ±1 ) extensiometer (Instron Corporation, MA, USA). The strain gauges were calibrated using static weight loading. The output from the strain gauges was captured using LabVIEW software (Labtech, USA) through a 16 channel multiplexer (Keithley, USA). Standard weights of 50 g (1.76 oz) to 250 g (8.82 oz) were added and the signal from the strain gauges was correlated to the applied load. The speed of the stepper motor was estimated by the extensiometer.

6 116 Computational Methods and Experiments in Material Characterisation II (a) (b) Figure 2: Schematic of the scissoring device (a) and identification of the pinch zone (PZ) (b).

7 Computational Methods and Experiments in Material Characterisation II 117 Cylindrical contacts of radius 5mm (1/5 ) and length 25mm (1 ) were machined and bolted onto the instrument arms. Surfaces were lubricated using a commercially available, petroleum based lubricant. A reasonable number of readings were taken (N=25) and results were analysed using the model above (eqn 1-5). The elastic constants were then compared to results from uniaxial testing. 5 Results and discussion A sample load calibration curve is presented in Fig 3. The response was very linear (R = 1.000) and the correction multiplier and offset are listed. It is anticipated that future routine calibration can be achieved using a set of standard elastomer samples Load [N] y = x R 2 = Strain gauge output [V] Figure 3: A sample calibration curve for the strain gauge determined by static loading of standard weights. Table 1 lists the elastic properties of both elastomers measured using the indentation instrument and the values determined by standard uniaxial testing. Results displayed good accuracy and precision, the latter by a 95% confidence interval. Implementation of the pinching deformation in this manner allowed for an insight into possible design issues of the surgical instrument. The scissoring movement was easy to employ, but a more linear travel may be possible by moving the bearing as far away from the tissue contacts as possible. The drive from the stepper motor seemed an unnecessary addition and it may possible for

8 118 Computational Methods and Experiments in Material Characterisation II the operator to close the contacts manually. This would have added advantages as the operator would develop an intuitive sense of the stiffness of the tissue and there would a smaller likelihood of damage to the tissue. A more compact handheld version of this device is not expected to add significantly to experimental error. Table 1: Elastic material constants determined by the instrument and standard compression testing. Nominal Strain Test Method: Nominal Thickness 1.6 mm 3 mm Standard Testing (N=25) 0% to 25% 0% to 25% Instrument (N=25) Young s Modulus Standard Testing (N=25) Neo-Hookean Constant C 10 Instrument (N=25) 1.21 MPa ± 0.07 MPa 1.34 MPa ± 0.03 MPa MPa ± 0.02 MPa MPa ± 0.01MPa Error 10% Error 4% 1.10 MPa 1.05 MPa MPa MPa ± 0.05 MPa ± 0.06 MPa ± 0.02 MPa ± 0.01 MPa Error (-)4% Error (-)6% Fig 4 shows a typical output signal from the instrument applied to a particular polymer sample, compared to the prediction of the analytical model. The result is very sensitive to accurate determination of the point of initial contact. This is difficult due to the highly nonlinear shape of the initial stages of deformation. An iterative technique has been developed to provide accurate determination of this point of contact (and the corresponding sample thickness), producing the results indicated. In general the current design of the apparatus proved sufficient for the laboratory, but the surgical environment requires sterilisation of all instruments. The sensitive parts of the instrument must be placed such that they are not damaged by a procedure such as autoclaving. 6 Conclusions The prototype device was very successful at delivering the cylindrical indentation to the elastomer samples. Results were consistent and accurate, suggesting that the concept has promise in the surgical environment. The

9 Computational Methods and Experiments in Material Characterisation II 119 prototype will be modified so it can hand-held and results can be compared to this study. The design must also be optimised for ease of sterilisation Load [N] Model Instrument Displacement [mm] Figure 4: A sample output from the instrument compared to the model prediction. Acknowledgement This project is supported by a grant from the Australian Research Council. References [1] Millard, R., The prevalence of urinary incontinence in Australia. Aust Continence J, (4): p [2] Maher, C., Female Urinary Incontinence. What causes it and how to treat it. Medicine Today, (2): p [3] Petros, P.E.P. and U. Ulmsten, An Integral Theory of Female Incontinence. Acta Obstet Gynaecol Scan, (Suppl 153): p [4] Petros, P.E.P. and U. Ulmsten, Part II. The biomechanics of vaginal tissue and supporting ligaments with special relevance to the pathogenesis of female urinary incontinence. Scand. J. Urol. Nephrol. Suppl., : p [5] Hayes, W.C., et al., A mathematical analysis for indentation tests of articular cartilage. J. Biomech, : p

10 120 Computational Methods and Experiments in Material Characterisation II [6] Lyyra, T., et al., Indentation instrument for the measurement of cartilage stiffness under arthroscopic control. Med. Eng Phys, (5): p [7] Toyras, J., et al., Technical Note: Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness. J. Biomech, : p [8] Kataoka, N., et al., Application of the pipette aspiration technique to the measurement of local elastic moduli of cholesterol-fed rabbit aortas. Theoretical and Applied Mechanics, : p [9] Lose, G., et al., New probe for measurement of related values of crosssectional area and pressure in a biological tube. Med. & Biol. Eng. & Comput, : p [10] Ghista, D.N., B.N. Rao, and A.S. H., In vivo elastic modulus of the left ventricle: its determination by means of a left ventricular vibrational model and its physiological significance and clinical utility. Med. Biol. Eng., (2): p [11] Alblas, J.B. and M. Kuipers, On the Two Dimensional Problem of a Cylindrical Stamp Pressed into a thin Elastic Layer. Acta Mech., : p [12] Alblas, J.B. and M. Kuipers, Contact Problems of a Rectangular Block on an Elastic Layer of Finite Thickness. Acta Mech., : p