- Email: [email protected]
Dynamic and quasi-static compressive response of porcine muscle
ARTICLE IN PRESS
Journal of Biomechanics 40 (2007) 2999–3005 www.elsevier.com/locate/jbiomech www.JBiomech.com
Dynamic and quasi-static compressive response of porcine muscle Bo Songa,, Weinong Chena, Yun Gea, Tusit Weerasooriyab a
School of Aeronautics & Astronautics and School of Materials Engineering, Purdue University, West Lafayette, IN, USA b US Army Research Laboratory, Aberdeen Proving Ground, MD, USA Accepted 5 February 2007
Abstract Research and application activities in impact biomechanics require dynamic response of biological tissues under high-rate loading. However, experimental difficulties have limited the characterization of soft tissues under such loading conditions. In this paper, we identify these technical challenges in dynamic compression experiments using a split Hopkinson pressure bar (SHPB) and present the remedies to overcome them. In order to subject the specimens to valid dynamic testing conditions, in addition to developing new pulseshaping techniques and incorporating highly sensitive load-measuring transducers, annular thin-disc specimens radically different from regular solid specimens were used to minimize radial inertia effects that may overshadow the intrinsic material properties. By using this modified SHPB, the compressive stress–strain behavior of soft porcine muscle tissue was obtained along and perpendicular to the muscle fiber direction from quasi-static to dynamic strain rates. The results show that the non-linear compressive stress–strain responses in both directions are strongly strain-rate sensitive. r 2007 Elsevier Ltd. All rights reserved. Keywords: Biological tissue; Porcine muscle; Dynamic behavior; Impact biomechanics; Split Hopkinson pressure bar (SHPB); Stress–strain; Strain rate
1. Introduction Recent rapid advances in tissue engineering and biomedical engineering require fundamental and quantitative understanding of mechanical properties of biological tissues. For example, in tissue engineering, tissues and organs that are repaired or replaced at surgeries are expected to have the same functions as the native ones (Butler et al., 2000). As the biomechanical properties of the tissues are critical to their functions (Butler et al., 2000), understanding the mechanical properties of the native tissues is essential to develop artificial or regenerative tissues with proper functions. Quasi-static response of biological tissues has been systematically studied since 1970s (Yamada, 1970; Fung, 1993). However, tissues are subjected not only to low-rate but also to high-rate loading in impact events, such as slip and falls, automobile and industrial accidents, sport and recreation accidents, blunt and ballistic impacts, and blasts from explosions. Since the Corresponding author. Tel.: +1 765 494 9354; fax: +1 765 494 9886.
E-mail address: [email protected] (B. Song). 0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.02.001
mechanical response of many body tissues is loading-rate sensitive, response of biological tissues under impact loading is necessary to understand injury mechanisms, to develop more human-like dummies, and to design efficient armors (King, 2000). A quantitative relationship between impact parameters (such as force, deformation, and acceleration) and injury is desired (King, 2000), and can be obtained using the response of the tissues to loadings at different strain rates. In many physiological, surgical, and medical device applications, it is required to use the stress–strain response at various strain rates to develop constitutive models (Sacks and Sun, 2003). There have been only a few attempts in the literature to characterize the response of soft tissues at different strain rates. Zheng et al. (1999) conducted ultrasound indentation experiments with a pen-size hand-held probe on human forearm and lower limb soft tissues at six different indentation rates from 0.75 to 7.5 mm/s. The amplitude of the loading pulses in ultrasonic experiments is inevitably very small and the strain rate varies periodically. Sinusoidal excitation up to 200 Hz was applied to dynamically characterize porcine muscle tissues in compression by Van
ARTICLE IN PRESS 3000
B. Song et al. / Journal of Biomechanics 40 (2007) 2999–3005
Loocke et al. (2006a). In these experiments, both strain rates and strains vary sinusoidally. Thus the results cannot be directly used for constitutive modeling. Investigation of mechanical properties at different rates of loading has also been carried out on spinal nerve roots subjected to tension at two different stretch rates, 0.01 and 15 mm/s, by Singh et al. (2006). However, very limited amount of dynamic mechanical characterization for stress–strain behavior at higher rates has been reported. McElhaney (1966) developed an air gun-type testing machine to obtain compressive stress–strain response of bovine muscle tissue at strain rates up to 1000 s1. This directimpact device may not generate evenly distributed testing conditions in the specimen at high rates. Shergold et al. (2006) characterized dynamic response of pig skin at high strain rates using a SHPB. SHPB has also been used to determine the high strain-rate compressive response of bovine muscle tissue by Sligtenhorst et al. (2006). Unlike in quasi-static experiments, inertia effects, which are typically negligible in material characterization, can overshadow the intrinsic mechanical behavior of the soft tissues deforming at high rates, resulting in invalid or inaccurate dynamic experimental data for the soft biological tissues. This motivates the development of more reliable dynamic experimental techniques for soft biological tissues. SHPB has been widely employed to investigate mechanical properties of engineering materials at high strain rates in the range of 102–104 s1 (Gray, 2000). However, when the specimen is a soft material, the resultant data from conventional SHPB tests may not be accurate or even valid due to the difficulties associated with dynamic stress equilibrium (or axial inertia effects) in specimen (Wu and Gorham, 1997; Gray and Blumenthal, 2000; Chen et al., 2002; Song and Chen, 2004). A test where the specimen deforms non-uniformly under non-equilibrated stress does not directly provide the constitutive behavior of the specimen material. The specimen should also deform at a nearly constant strain rate to identify strain-rate effects (Chen et al., 2002; Song and Chen, 2005). When the SHPB is used to characterize very soft materials, radial inertia effects in specimen must be minimized because the radial inertia induces an extra stress in the same order of magnitude as their mechanical response (Kolsky, 1949; Davies and Hunter, 1963; Gorham, 1989; Forrestal et al., 2007; Song et al., 2006, 2007). Therefore, the conventional SHPB must be modified to obtain accurate intrinsic mechanical response of soft biological tissues. In the following, the modifications that were incorporated to the conventional SHPB for high-rate characterization of soft biological tissues are presented. Then, we used the modified SHPB to obtain compressive stress–strain curves for porcine muscle tissues along and perpendicular to the fiber direction, at different dynamic strain rates. In addition, quasi-static stress–strain response was experimentally obtained using a standard MTS machine. This paper also presents the strain-rate effects on the deforma-
tion responses of the muscle in both fiber and perpendicular to the fiber directions.
2. SHPB modified for soft biological tissue characterization The conventional SHPB has been well reviewed and documented in recent years (Gray, 2000). In a typical conventional SHPB experiment, the impact of the striker on the end of the incident bar generates an elastic wave (incident wave), which propagates through the incident bar. When this incident wave travels to the specimen, the incident wave is partly reflected back and partly transmitted into the transmission bar compressing the specimen. During this compression, the specimen must be in a state of dynamic stress equilibrium (Kolsky, 1949) such that the dynamic response averaged over the volume of specimen can be treated as the pointwise material behavior. Dynamic stress equilibrium is, in general, achieved very quickly in a metallic specimen (Gray, 2000). However, when the specimen is a soft biological tissue, the equilibrated stress state in the specimen during dynamic deformation may not be achieved over the entire loading duration due to the low wave speeds in soft materials (Song and Chen, 2004). The modifications necessary to reach dynamic axial stress equilibrium in soft materials include using a thin specimen and pulse-shaping techniques (Chen et al., 2002; Song and Chen, 2004). Pulse-shaping techniques that employ a pulse shaper at the impact end of the incident bar have recently been developed to generate an initially slow loading profile in the incident pulse to reach early dynamic stress equilibrium (Chen et al., 2002; Song and Chen, 2004). Through proper combination of material and dimensions of the pulse shaper and striking speed of the striker, an appropriate pulse-shaping design is capable of modifying the profile of the incident pulse to facilitate not only dynamic stress equilibrium, but also a nearly constant strain-rate deformation in specimen (Chen et al., 2002; Song and Chen, 2005). In order to reach a high signal-tonoise ratio during experiments where the load signals are very small, low-impedance bar materials and high-sensitivity transducers have been employed as discussed elsewhere (Chen et al., 1999, 2000; Gray and Blumenthal, 2000). It has been recently observed that accurate dynamic experimental data may not be obtained when extra-soft materials such as muscles are characterized even with the modified SHPB (Moy et al., 2006; Song et al., 2006, 2007). Even though the pulse-shaping techniques and a thin specimen are used to facilitate valid testing conditions, an abnormal spike-like feature was observed in the force history measured from a ballistic gelatin (Moy et al., 2006). When the SHPB was used to conduct dynamic experiments on porcine muscle, the spike also appeared at the early stage of the stress history, as shown in Fig. 1. This spikelike feature has been determined not as a part of the intrinsic response of the material. Instead, it is the result of
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In summary, in order to ensure the biological tissue specimen to deform at a nearly constant strain rate under dynamic stress equilibrium and to minimize the radial inertia effects, a thin annular disc specimen and a proper pulse-shaping design are required. 3. Experiments 3.1. Specimen preparation
Fig. 1. Experimental record of incident, reflected, and transmitted pulses from a conventional SHPB experiment on a solid porcine muscle specimen.
radial inertia in specimen during high-rate axial compression (Moy et al., 2006; Song et al, 2006, 2007). The radial inertia in specimen during a SHPB experiment has been studied for decades starting from Kolsky (1949) and was investigated most recently by Forrestal et al. (2007). The radial inertia in specimen brings an extra axial stress component. The distribution of the inertiainduced axial stress, s1z , along the radial direction was found to be parabolic, with its maximum value reached at the specimen center and zero value at the cylindrical surface (Forrestal et al., 2007). The additional axial stress averaged over the specimen cross-section is (Kolsky, 1949; Forrestal et al., 2007) s¯ 1z ¼
a2 rs €, 8
The porcine muscle was cut from a ham of a 5-monthold female swine immediately after it was slaughtered. The muscle was marinated in a modified Kreb solution (136 mM NaCl, 4 mM KCl, 2.35 mM CaCl2, 1 mM NaH2PO4, 0.85 mM MgCl2, 12 mM NaHCO3, 5 mM glucose, and pH ¼ 7.4) bubbled with 95% O2 and 5% CO2 at the swine body temperature of 39.2 1C (Lo´pez et al., 1988). Just before subjected to mechanical loading, the muscles were sliced with an electric food slicer (Black & Decker) into 3.2-mm-thick flat sheets along and perpendicular to fiber directions. Annular-shaped specimens were then cut from the flat sheets. We used 10.0 and 3.0 mm diameter trephine blades with very sharp edges (Medtronic
(1)
where a is the radius of the specimen, rs is the density of the specimen material, and € is the specimen’s axial strain acceleration. Eq. (1) shows that this average extra stress exists no matter what specimen material is being tested. The additional stress in a specimen tested with a typical conventional SHPB, which has a diameter of 10 mm and a material density in the order of 2000 kg/m3, is estimated to be in the order of 2 MPa. This additional axial stress (2 MPa) may be negligible when testing regular engineering materials. However, it could overshadow the intrinsic response of soft biological tissues such as porcine muscle with the strength of a few MPa. The inertia-induced stress has been minimized through further modifications to the SHPB by using an annular specimen and decreasing the axial strain acceleration in the specimen (Moy et al., 2006; Song et al., 2006, 2007). A parametric study also indicates that the inertia-induced stress in an annular specimen decreases rapidly as the inner radius reaches about 30% of the outer radius (Ge et al., 2006; Song et al., 2007).
Fig. 2. Schematic and photograph of an annular porcine muscle specimen used for dynamic experiments in this study.
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Ophthalmics) to cut the annular tissue specimens for dynamic experiments, a schematic of which is shown in Fig. 2(a). Fig. 2(b) shows a photograph of an actual specimen. Since the radial inertia is negligible in quasistatic experiments, the specimens for these MTS experiments were made into 3.2 mm thick solid disks with an outer diameter of 10.00 mm. 3.2. Experimental setup The schematic of the modified SHPB is shown in Fig. 3. The 7075-T6 19 mm diameter aluminum incident and transmission bars are 3658 and 2134 mm long, respectively. A pair of semi-conductor strain gages (Kyowa Electronics Instruments, Co. Ltd.) were used on the transmission bar to record the weak signals transmitted from the soft specimen. Two pairs of regular resistive foil strain gages (Vishay Measurements Group) were attached in the middle and close to the impact end of the incident bar. The usage of the strain gages at the middle location follows the regular SHPB method. The strain gages close to the impact end of the incident bar were employed to record extended loading duration, which is needed to produce relatively large strains in the specimen at relatively low strain rates (i.e., 450 s1 in this study) (Chen and Song, 2005). Annealed copper disks and tubes were used as the pulse shapers to facilitate dynamic stress equilibrium, to obtain nearly constant strain rate of deformation, and to minimize the radial inertia in the specimens. When the specimen deforms under dynamic stress equilibrium, the strain rate, strain, and stress histories in the specimen can be calculated using the following equations, respectively (Gray, 2000): _ ¼ 2
C0 r ðtÞ, Ls
¼ 2
C0 Ls
s¼
Z
where r ðtÞ and t ðtÞ are reflected and transmitted strain histories, respectively; A0 is the cross-sectional area of the bars; E0 and C 0 are Young’s modulus and elastic wave speed in the bar material, respectively; As and Ls are initial cross-sectional area and length of the specimen, respectively. When the material under investigation is so soft that the reflected pulse is nearly the same as the incident pulse, the strain rate and strain histories in specimen are calculated by simply using the incident pulse. The incident, reflected, and transmitted pulses from a typical high-rate experiment are shown in Fig. 4. The traces in Fig. 4 show that the initial strain acceleration is lowered through proper pulse shaping. The high-frequency oscillations commonly encountered in conventional SHPB tests (Fig. 1) are nearly eliminated from all three measured stress pulses (Fig. 4). Such a clean loading history facilitates accurate characterization of the specimen material response at this high strain rate. The dynamic stress equilibrium was also checked using the quartz crystal force transducers embedded near the specimen as shown in Fig. 3 (Chen et al., 2002), and the results associated are shown in Fig. 5. The X-cut circular piezoelectric quartz crystal force
(2)
t
r ðtÞ dt,
(3)
0
A0 E 0 t ðtÞ, As
(4)
Fig. 4. A typical set of incident, reflected, and transmitted pulses obtained from the modified SHPB experiment on an annular porcine muscle specimen.
Fig. 3. Schematic of a modified SHPB for testing soft biological tissues.
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Fig. 5. Dynamic stress equilibrium process in the porcine muscle specimen.
Fig. 6. Strain rate and strain histories in the porcine muscle specimen.
transducers (Boston Piezo-Optics Inc.) had a mechanical impedance very close to the aluminum bar material, such that the propagation of stress wave in the bars are not to be affected. The axial inertia in the aluminum disk on top of the quartz crystals has been compensated by using three quartz transducers (Casem et al., 2005). The stress measurement by the quartz crystals may still reflect complicated stress states at bar ends with noise-like oscillations in the loading histories. In this study, we used the quartz readings only for the purpose of comparing stress histories. The specimen axial stress was calculated using the semi-conductor strain gage readings from the transmission bar where the stress waves become close to one dimensional. The fact that the stress histories at both end faces of the tissue specimen overlap each other indicates that the specimen deforms under a dynamically equilibrated stress
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Fig. 7. Typical raw and smoothed stress–strain curves.
during the impact loading. Furthermore, the initial spike in the stress histories shown in Fig. 1 has already been minimized by using the pulse-shaping technique and the annular specimen. Fig. 6 shows the strain rate and strain histories in specimen, which indicate that the specimen deformed at a nearly constant strain rate of 3650 s1. Even though the stress history recorded in the transmission bar is nearly one dimensional, there are still small oscillations riding on the main signal. We smoothened these local oscillations in the presentation of the stress–strain behavior such that the average stress–strain curve could be obtained from a batch of experiments under identical testing conditions. However, in some cases, these oscillations may reflect local deformation states in the specimen. For a complete documentation of the experimental data, we show in Fig. 7 typical raw and smoothed stress–strain curves at the strain rate of 3650 s1. Dynamic experiments were conducted at three dynamic strain rates for the porcine muscle tissue in each direction along and perpendicular to the fibers. In order to determine the strain-rate effects of the porcine muscle tissue in a wider strain rate range, we also conducted quasi-static experiments using a hydraulically driven machine (MTS 810). The MTS was set to the mode of displacement control at two speeds, which correspond to the strain rates 7 103 and 7 102 s1. 4. Results and discussion The resultant compressive stress–strain curves are presented in Figs. 8 and 9 for loading directions along the muscle fiber direction and perpendicular to it, respectively. Each of the curves in these two figures are the average of at least five repeated experiments conducted under identical loading conditions, except for the lowest strain rate (7 103 s1) case, where only four repeated
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Fig. 8. Stress–strain curves of the porcine muscle along fiber direction at various strain rates.
Fig. 9. Stress–strain curves of the porcine muscle perpendicular to fiber direction at various strain rates.
experiments were performed due to time constraints. Error bars were plotted on each mean stress–strain curve to show data scatter under identical testing conditions. All stress– strain curves exhibit a toe region at the beginning, followed by a transitional non-linear response and then a strainhardening behavior, which are similar to those obtained previously in quasi-static experiments (Zheng et al., 1999; Van Loocke et al., 2006b). Our stress–strain data for the porcine muscle at quasi-static strain rates are very close to the data obtained from the indentation experiments on human forearm and lower limb soft tissues by Zheng et al. (1999). However, our data are stiffer than those obtained from quasi-static experiments on porcine fresh muscle tissues by Van Loocke et al. (2006b). This is perhaps because of different samples and testing conditions. Van Loocke et al. (2006b) used fresh muscles from a pelvic limb of 3-month-old male pigs for quasi-static experiments at
the strain rate of 0.0005 s1. However, our quasi-static experiments were conducted on the fresh muscles from a ham of a 5-month-old female pig at one and two orders of magnitudes higher strain rates. It should be noted that the testing conditions in the dynamic experiments conducted by Zheng et al. (1999) and Van Loocke et al. (2006a) are quite different from our constant high-rate experiments. This loading condition difference makes the direct comparison of resultant data inappropriate. Sligtenhorst et al. (2006) conducted high-rate testing of bovine muscle tissue by using the SHPB. Compared to their high-rate stress– strain data, the stress response for the porcine muscle tissue in this study is much lower. However, our data are very close to those for bovine muscle tissue, which was sliced perpendicular to the long axis of the bone, obtained by McElhaney (1966) over a strain rate ranging from 0.001 to 1000 s1. The stress response for the porcine muscle tissue is slightly lower than that for the bovine muscle tissue possibly because of different samples and sample conditions. Even though the similar loading devices are used, valid testing conditions are critical to obtain intrinsic material response. In this study, we employed modifications to the SHPB and specimen geometry to ensure valid testing conditions such that accurate stress–strain response for the porcine muscle tissue was obtained. Figs. 10 and 11 show the trends of stress versus strain rate at the engineering strain of 10%, 25%, and 45% along both directions in the porcine muscle tissue. The data for bovine muscle tissue by McElhaney are also plotted in both figures for comparison purposes. The strain-rate sensitivities for both the porcine muscle tissue and the bovine muscle tissue are observed to be consistent. Strain rate effects are apparent in the porcine muscle tissue studied in this research. The strain-rate dependency is clearly sensitive to the loading direction. The strain-rate sensitivity along the perpendicular direction is more significant than that along the fiber direction. The availability of stress–strain data for
Fig. 10. Strain rate effects of the porcine muscle along fiber direction.
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Fig. 11. Strain rate effects of the porcine muscle perpendicular to fiber direction.
the porcine muscle tissue over a wide range of strain rates is expected to make developing accurate strain-rate-dependent tissue models possible in the future. Acknowledgments This research was supported by US Army Research Laboratory (ARL) through a collaborative research agreement with Purdue University. The authors wish to thank Mr. Yi Pan and Mr. Chul Jin Syn for their efforts in the quasi-static experiments. References Butler, D.L., Goldstein, S.A., Guilak, F., 2000. Functional tissue engineering: the role of biomechanics. Transactions of the ASME, Journal of Biomechanical Engineering 122, 570–575. Casem, D., Weerasooriya, T., Moy, P., 2005. Inertia effects of quartz force transducers embedded in a split Hopkinson pressure bar. Experimental Mechanics 45, 368–376. Chen, W., Song, B., 2005. Dynamic compression testing on polymeric foams. In: Experiments in Automotive Engineering—Optical Techniques, 2005 SAE World Congress, April 11–14, 2005, Detroit, MI, USA. Chen, W., Zhang, B., Forrestal, M.J., 1999. A split Hopkinson bar technique for low-impedance materials. Experimental Mechanics 39, 81–85. Chen, W., Lu, F., Zhou, B., 2000. A quartz-crystal-embedded split Hopkinson pressure bar for soft materials. Experimental Mechanics 40, 1–6. Chen, W., Lu, F., Frew, D.J., Forrestal, M.J., 2002. Dynamic compression testing of soft materials. Transactions of the ASME, Journal of Applied Mechanics 69, 214–223. Davies, E., Hunter, S.C., 1963. The dynamic compression testing of solids by the method of the split Hopkinson pressure bar. Journal of the Mechanics and Physics of Solids 11, 155–179. Forrestal, M.J., Wright, T.W., Chen, W., 2007. The effect of radial inertia on brittle samples during the split Hopkinson pressure bar test. International Journal of Impact Engineering 34, 405–411.
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Fung, Y.C., 1993. Biomechanics: Mechanical Properties of Living Tissues, second ed. Springer, New York. Ge, Y., Chen, W., Weerasooriya, T., 2006. Radial inertia effects on dynamic response of soft biological tissues. In: Proceedings of the SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 4–7, 2006, St. Louis, MO. Gorham, D.A., 1989. Specimen inertia in high strain-rate compression. Journal of Physics D: Applied Physics 22, 1888–1893. Gray, G.T., 2000. Classic split-Hopkinson pressure bar testing. ASM Handbook, Mechanical Testing and Evaluation, vol. 8, Materials Park, OH, pp. 462–476. Gray, G.T., Blumenthal, W.R., 2000. Split-Hopkinson pressure bar testing of soft materials. ASM Handbook, Mechanical Testing and Evaluation, Materials Park, OH, 8, 488–496. King, A.I., 2000. Fundamentals of impact biomechanics: Part I— biomechanics of the head, neck, and thorax. Annual Review of Biomedical Engineering 2, 55–81. Kolsky, H., 1949. An investigation of the mechanical properties of meterials at very high rates of loading. Proceedings of the Physical Society of London B 62, 679–700. Lo´pez, J.R., Allen, P.D., Alamo, L., Jones, D., Sreter, F.A., 1988. Myoplasmic free [Ca2+] during a malignant hyperthermia episode in swine. Muscle and Nerve 11, 82–88. McElhaney, J., 1966. Dynamic response of bone and muscle tissue. Journal of Applied Physiology 21, 1231–1236. Moy, P., Weerasooriya, T., Juliano, T.F., VanLandingham, M.R., 2006. Dynamic response of an alternative tissue simulant, physically associating gels (PAG), In: Proceedings of the SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 4–7, 2006, St. Louis, MO. Sacks, M.S., Sun, W., 2003. Multiaxial mechanical behavior of biological materials. Annual Review of Biomedical Engineering 5, 251–284. Shergold, O.A., Fleck, N.A., Radford, D., 2006. The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. International Journal Impact Engineering 32, 1384–1402. Singh, A., Lu, Y., Chen, C., Cavanaugh, J.M., 2006. Mechanical properties of spinal nerve roots subjected to tension at different strain rates. Journal of Biomechanics 39, 1669–1676. Sligtenhorst, C.V., Cronin, D.S., Brodland, G.W., 2006. High strain rate compressive properties of bovine muscle tissue determined using a split Hopkinson bar apparatus. Journal of Biomechanics 39, 1852–1858. Song, B., Chen, W., 2004. Dynamic stress equilibration in split Hopkinson pressure tests on soft materials. Experimental Mechanics 44, 300–312. Song, B., Chen, W., 2005. Split Hopkinson pressure bar techniques for characterizing soft materials. Latin American Journal of Solids and Structures 2, 113–152. Song, B., Chen, W., Weerasooriya, T., 2006. Experimental investigation of radial inertia effects in Hopkinson bar testing of extra-soft materials. In: Proceedings of the SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 4–7, 2006, St. Louis, MO. Song, B., Ge, Y., Chen, W.W., Weerasooriya, T., 2007. Radial inertia effects in Kolsky bar testing of extra-soft specimens. Experimental Mechanics (in press). Van Loocke, M., Simms, C.K., Lyons, C.G., 2006a. On the elastic and viscoelastic properties of passive muscle tissue in compression. Journal of Biomechanics 39, S36–S37. Van Loocke, M., Simms, C.K., Lyons, C.G., 2006b. A validated model of passive muscle in compression. Journal of Biomechanics 39, 2999–3009. Wu, X.J., Gorham, D.A., 1997. Stress equilibrium in the split Hopkinson pressure bar test. Journal de Physique IV France C 3, 91–96. Yamada, H., 1970. Strength of Biological Materials. Williams & Wilkins Co, Baltimore. Zheng, Y., Mak, A.F.T., Lue, B., 1999. Objective assessment of limb tissue elasticity: development of a manual indentation procedure. Journal of Rehabilitation Research and Development 36, 71–85.
Journal of Biomechanics 40 (2007) 2999–3005 www.elsevier.com/locate/jbiomech www.JBiomech.com
Dynamic and quasi-static compressive response of porcine muscle Bo Songa,, Weinong Chena, Yun Gea, Tusit Weerasooriyab a
School of Aeronautics & Astronautics and School of Materials Engineering, Purdue University, West Lafayette, IN, USA b US Army Research Laboratory, Aberdeen Proving Ground, MD, USA Accepted 5 February 2007
Abstract Research and application activities in impact biomechanics require dynamic response of biological tissues under high-rate loading. However, experimental difficulties have limited the characterization of soft tissues under such loading conditions. In this paper, we identify these technical challenges in dynamic compression experiments using a split Hopkinson pressure bar (SHPB) and present the remedies to overcome them. In order to subject the specimens to valid dynamic testing conditions, in addition to developing new pulseshaping techniques and incorporating highly sensitive load-measuring transducers, annular thin-disc specimens radically different from regular solid specimens were used to minimize radial inertia effects that may overshadow the intrinsic material properties. By using this modified SHPB, the compressive stress–strain behavior of soft porcine muscle tissue was obtained along and perpendicular to the muscle fiber direction from quasi-static to dynamic strain rates. The results show that the non-linear compressive stress–strain responses in both directions are strongly strain-rate sensitive. r 2007 Elsevier Ltd. All rights reserved. Keywords: Biological tissue; Porcine muscle; Dynamic behavior; Impact biomechanics; Split Hopkinson pressure bar (SHPB); Stress–strain; Strain rate
1. Introduction Recent rapid advances in tissue engineering and biomedical engineering require fundamental and quantitative understanding of mechanical properties of biological tissues. For example, in tissue engineering, tissues and organs that are repaired or replaced at surgeries are expected to have the same functions as the native ones (Butler et al., 2000). As the biomechanical properties of the tissues are critical to their functions (Butler et al., 2000), understanding the mechanical properties of the native tissues is essential to develop artificial or regenerative tissues with proper functions. Quasi-static response of biological tissues has been systematically studied since 1970s (Yamada, 1970; Fung, 1993). However, tissues are subjected not only to low-rate but also to high-rate loading in impact events, such as slip and falls, automobile and industrial accidents, sport and recreation accidents, blunt and ballistic impacts, and blasts from explosions. Since the Corresponding author. Tel.: +1 765 494 9354; fax: +1 765 494 9886.
E-mail address: [email protected] (B. Song). 0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.02.001
mechanical response of many body tissues is loading-rate sensitive, response of biological tissues under impact loading is necessary to understand injury mechanisms, to develop more human-like dummies, and to design efficient armors (King, 2000). A quantitative relationship between impact parameters (such as force, deformation, and acceleration) and injury is desired (King, 2000), and can be obtained using the response of the tissues to loadings at different strain rates. In many physiological, surgical, and medical device applications, it is required to use the stress–strain response at various strain rates to develop constitutive models (Sacks and Sun, 2003). There have been only a few attempts in the literature to characterize the response of soft tissues at different strain rates. Zheng et al. (1999) conducted ultrasound indentation experiments with a pen-size hand-held probe on human forearm and lower limb soft tissues at six different indentation rates from 0.75 to 7.5 mm/s. The amplitude of the loading pulses in ultrasonic experiments is inevitably very small and the strain rate varies periodically. Sinusoidal excitation up to 200 Hz was applied to dynamically characterize porcine muscle tissues in compression by Van
ARTICLE IN PRESS 3000
B. Song et al. / Journal of Biomechanics 40 (2007) 2999–3005
Loocke et al. (2006a). In these experiments, both strain rates and strains vary sinusoidally. Thus the results cannot be directly used for constitutive modeling. Investigation of mechanical properties at different rates of loading has also been carried out on spinal nerve roots subjected to tension at two different stretch rates, 0.01 and 15 mm/s, by Singh et al. (2006). However, very limited amount of dynamic mechanical characterization for stress–strain behavior at higher rates has been reported. McElhaney (1966) developed an air gun-type testing machine to obtain compressive stress–strain response of bovine muscle tissue at strain rates up to 1000 s1. This directimpact device may not generate evenly distributed testing conditions in the specimen at high rates. Shergold et al. (2006) characterized dynamic response of pig skin at high strain rates using a SHPB. SHPB has also been used to determine the high strain-rate compressive response of bovine muscle tissue by Sligtenhorst et al. (2006). Unlike in quasi-static experiments, inertia effects, which are typically negligible in material characterization, can overshadow the intrinsic mechanical behavior of the soft tissues deforming at high rates, resulting in invalid or inaccurate dynamic experimental data for the soft biological tissues. This motivates the development of more reliable dynamic experimental techniques for soft biological tissues. SHPB has been widely employed to investigate mechanical properties of engineering materials at high strain rates in the range of 102–104 s1 (Gray, 2000). However, when the specimen is a soft material, the resultant data from conventional SHPB tests may not be accurate or even valid due to the difficulties associated with dynamic stress equilibrium (or axial inertia effects) in specimen (Wu and Gorham, 1997; Gray and Blumenthal, 2000; Chen et al., 2002; Song and Chen, 2004). A test where the specimen deforms non-uniformly under non-equilibrated stress does not directly provide the constitutive behavior of the specimen material. The specimen should also deform at a nearly constant strain rate to identify strain-rate effects (Chen et al., 2002; Song and Chen, 2005). When the SHPB is used to characterize very soft materials, radial inertia effects in specimen must be minimized because the radial inertia induces an extra stress in the same order of magnitude as their mechanical response (Kolsky, 1949; Davies and Hunter, 1963; Gorham, 1989; Forrestal et al., 2007; Song et al., 2006, 2007). Therefore, the conventional SHPB must be modified to obtain accurate intrinsic mechanical response of soft biological tissues. In the following, the modifications that were incorporated to the conventional SHPB for high-rate characterization of soft biological tissues are presented. Then, we used the modified SHPB to obtain compressive stress–strain curves for porcine muscle tissues along and perpendicular to the fiber direction, at different dynamic strain rates. In addition, quasi-static stress–strain response was experimentally obtained using a standard MTS machine. This paper also presents the strain-rate effects on the deforma-
tion responses of the muscle in both fiber and perpendicular to the fiber directions.
2. SHPB modified for soft biological tissue characterization The conventional SHPB has been well reviewed and documented in recent years (Gray, 2000). In a typical conventional SHPB experiment, the impact of the striker on the end of the incident bar generates an elastic wave (incident wave), which propagates through the incident bar. When this incident wave travels to the specimen, the incident wave is partly reflected back and partly transmitted into the transmission bar compressing the specimen. During this compression, the specimen must be in a state of dynamic stress equilibrium (Kolsky, 1949) such that the dynamic response averaged over the volume of specimen can be treated as the pointwise material behavior. Dynamic stress equilibrium is, in general, achieved very quickly in a metallic specimen (Gray, 2000). However, when the specimen is a soft biological tissue, the equilibrated stress state in the specimen during dynamic deformation may not be achieved over the entire loading duration due to the low wave speeds in soft materials (Song and Chen, 2004). The modifications necessary to reach dynamic axial stress equilibrium in soft materials include using a thin specimen and pulse-shaping techniques (Chen et al., 2002; Song and Chen, 2004). Pulse-shaping techniques that employ a pulse shaper at the impact end of the incident bar have recently been developed to generate an initially slow loading profile in the incident pulse to reach early dynamic stress equilibrium (Chen et al., 2002; Song and Chen, 2004). Through proper combination of material and dimensions of the pulse shaper and striking speed of the striker, an appropriate pulse-shaping design is capable of modifying the profile of the incident pulse to facilitate not only dynamic stress equilibrium, but also a nearly constant strain-rate deformation in specimen (Chen et al., 2002; Song and Chen, 2005). In order to reach a high signal-tonoise ratio during experiments where the load signals are very small, low-impedance bar materials and high-sensitivity transducers have been employed as discussed elsewhere (Chen et al., 1999, 2000; Gray and Blumenthal, 2000). It has been recently observed that accurate dynamic experimental data may not be obtained when extra-soft materials such as muscles are characterized even with the modified SHPB (Moy et al., 2006; Song et al., 2006, 2007). Even though the pulse-shaping techniques and a thin specimen are used to facilitate valid testing conditions, an abnormal spike-like feature was observed in the force history measured from a ballistic gelatin (Moy et al., 2006). When the SHPB was used to conduct dynamic experiments on porcine muscle, the spike also appeared at the early stage of the stress history, as shown in Fig. 1. This spikelike feature has been determined not as a part of the intrinsic response of the material. Instead, it is the result of
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In summary, in order to ensure the biological tissue specimen to deform at a nearly constant strain rate under dynamic stress equilibrium and to minimize the radial inertia effects, a thin annular disc specimen and a proper pulse-shaping design are required. 3. Experiments 3.1. Specimen preparation
Fig. 1. Experimental record of incident, reflected, and transmitted pulses from a conventional SHPB experiment on a solid porcine muscle specimen.
radial inertia in specimen during high-rate axial compression (Moy et al., 2006; Song et al, 2006, 2007). The radial inertia in specimen during a SHPB experiment has been studied for decades starting from Kolsky (1949) and was investigated most recently by Forrestal et al. (2007). The radial inertia in specimen brings an extra axial stress component. The distribution of the inertiainduced axial stress, s1z , along the radial direction was found to be parabolic, with its maximum value reached at the specimen center and zero value at the cylindrical surface (Forrestal et al., 2007). The additional axial stress averaged over the specimen cross-section is (Kolsky, 1949; Forrestal et al., 2007) s¯ 1z ¼
a2 rs €, 8
The porcine muscle was cut from a ham of a 5-monthold female swine immediately after it was slaughtered. The muscle was marinated in a modified Kreb solution (136 mM NaCl, 4 mM KCl, 2.35 mM CaCl2, 1 mM NaH2PO4, 0.85 mM MgCl2, 12 mM NaHCO3, 5 mM glucose, and pH ¼ 7.4) bubbled with 95% O2 and 5% CO2 at the swine body temperature of 39.2 1C (Lo´pez et al., 1988). Just before subjected to mechanical loading, the muscles were sliced with an electric food slicer (Black & Decker) into 3.2-mm-thick flat sheets along and perpendicular to fiber directions. Annular-shaped specimens were then cut from the flat sheets. We used 10.0 and 3.0 mm diameter trephine blades with very sharp edges (Medtronic
(1)
where a is the radius of the specimen, rs is the density of the specimen material, and € is the specimen’s axial strain acceleration. Eq. (1) shows that this average extra stress exists no matter what specimen material is being tested. The additional stress in a specimen tested with a typical conventional SHPB, which has a diameter of 10 mm and a material density in the order of 2000 kg/m3, is estimated to be in the order of 2 MPa. This additional axial stress (2 MPa) may be negligible when testing regular engineering materials. However, it could overshadow the intrinsic response of soft biological tissues such as porcine muscle with the strength of a few MPa. The inertia-induced stress has been minimized through further modifications to the SHPB by using an annular specimen and decreasing the axial strain acceleration in the specimen (Moy et al., 2006; Song et al., 2006, 2007). A parametric study also indicates that the inertia-induced stress in an annular specimen decreases rapidly as the inner radius reaches about 30% of the outer radius (Ge et al., 2006; Song et al., 2007).
Fig. 2. Schematic and photograph of an annular porcine muscle specimen used for dynamic experiments in this study.
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Ophthalmics) to cut the annular tissue specimens for dynamic experiments, a schematic of which is shown in Fig. 2(a). Fig. 2(b) shows a photograph of an actual specimen. Since the radial inertia is negligible in quasistatic experiments, the specimens for these MTS experiments were made into 3.2 mm thick solid disks with an outer diameter of 10.00 mm. 3.2. Experimental setup The schematic of the modified SHPB is shown in Fig. 3. The 7075-T6 19 mm diameter aluminum incident and transmission bars are 3658 and 2134 mm long, respectively. A pair of semi-conductor strain gages (Kyowa Electronics Instruments, Co. Ltd.) were used on the transmission bar to record the weak signals transmitted from the soft specimen. Two pairs of regular resistive foil strain gages (Vishay Measurements Group) were attached in the middle and close to the impact end of the incident bar. The usage of the strain gages at the middle location follows the regular SHPB method. The strain gages close to the impact end of the incident bar were employed to record extended loading duration, which is needed to produce relatively large strains in the specimen at relatively low strain rates (i.e., 450 s1 in this study) (Chen and Song, 2005). Annealed copper disks and tubes were used as the pulse shapers to facilitate dynamic stress equilibrium, to obtain nearly constant strain rate of deformation, and to minimize the radial inertia in the specimens. When the specimen deforms under dynamic stress equilibrium, the strain rate, strain, and stress histories in the specimen can be calculated using the following equations, respectively (Gray, 2000): _ ¼ 2
C0 r ðtÞ, Ls
¼ 2
C0 Ls
s¼
Z
where r ðtÞ and t ðtÞ are reflected and transmitted strain histories, respectively; A0 is the cross-sectional area of the bars; E0 and C 0 are Young’s modulus and elastic wave speed in the bar material, respectively; As and Ls are initial cross-sectional area and length of the specimen, respectively. When the material under investigation is so soft that the reflected pulse is nearly the same as the incident pulse, the strain rate and strain histories in specimen are calculated by simply using the incident pulse. The incident, reflected, and transmitted pulses from a typical high-rate experiment are shown in Fig. 4. The traces in Fig. 4 show that the initial strain acceleration is lowered through proper pulse shaping. The high-frequency oscillations commonly encountered in conventional SHPB tests (Fig. 1) are nearly eliminated from all three measured stress pulses (Fig. 4). Such a clean loading history facilitates accurate characterization of the specimen material response at this high strain rate. The dynamic stress equilibrium was also checked using the quartz crystal force transducers embedded near the specimen as shown in Fig. 3 (Chen et al., 2002), and the results associated are shown in Fig. 5. The X-cut circular piezoelectric quartz crystal force
(2)
t
r ðtÞ dt,
(3)
0
A0 E 0 t ðtÞ, As
(4)
Fig. 4. A typical set of incident, reflected, and transmitted pulses obtained from the modified SHPB experiment on an annular porcine muscle specimen.
Fig. 3. Schematic of a modified SHPB for testing soft biological tissues.
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Fig. 5. Dynamic stress equilibrium process in the porcine muscle specimen.
Fig. 6. Strain rate and strain histories in the porcine muscle specimen.
transducers (Boston Piezo-Optics Inc.) had a mechanical impedance very close to the aluminum bar material, such that the propagation of stress wave in the bars are not to be affected. The axial inertia in the aluminum disk on top of the quartz crystals has been compensated by using three quartz transducers (Casem et al., 2005). The stress measurement by the quartz crystals may still reflect complicated stress states at bar ends with noise-like oscillations in the loading histories. In this study, we used the quartz readings only for the purpose of comparing stress histories. The specimen axial stress was calculated using the semi-conductor strain gage readings from the transmission bar where the stress waves become close to one dimensional. The fact that the stress histories at both end faces of the tissue specimen overlap each other indicates that the specimen deforms under a dynamically equilibrated stress
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Fig. 7. Typical raw and smoothed stress–strain curves.
during the impact loading. Furthermore, the initial spike in the stress histories shown in Fig. 1 has already been minimized by using the pulse-shaping technique and the annular specimen. Fig. 6 shows the strain rate and strain histories in specimen, which indicate that the specimen deformed at a nearly constant strain rate of 3650 s1. Even though the stress history recorded in the transmission bar is nearly one dimensional, there are still small oscillations riding on the main signal. We smoothened these local oscillations in the presentation of the stress–strain behavior such that the average stress–strain curve could be obtained from a batch of experiments under identical testing conditions. However, in some cases, these oscillations may reflect local deformation states in the specimen. For a complete documentation of the experimental data, we show in Fig. 7 typical raw and smoothed stress–strain curves at the strain rate of 3650 s1. Dynamic experiments were conducted at three dynamic strain rates for the porcine muscle tissue in each direction along and perpendicular to the fibers. In order to determine the strain-rate effects of the porcine muscle tissue in a wider strain rate range, we also conducted quasi-static experiments using a hydraulically driven machine (MTS 810). The MTS was set to the mode of displacement control at two speeds, which correspond to the strain rates 7 103 and 7 102 s1. 4. Results and discussion The resultant compressive stress–strain curves are presented in Figs. 8 and 9 for loading directions along the muscle fiber direction and perpendicular to it, respectively. Each of the curves in these two figures are the average of at least five repeated experiments conducted under identical loading conditions, except for the lowest strain rate (7 103 s1) case, where only four repeated
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Fig. 8. Stress–strain curves of the porcine muscle along fiber direction at various strain rates.
Fig. 9. Stress–strain curves of the porcine muscle perpendicular to fiber direction at various strain rates.
experiments were performed due to time constraints. Error bars were plotted on each mean stress–strain curve to show data scatter under identical testing conditions. All stress– strain curves exhibit a toe region at the beginning, followed by a transitional non-linear response and then a strainhardening behavior, which are similar to those obtained previously in quasi-static experiments (Zheng et al., 1999; Van Loocke et al., 2006b). Our stress–strain data for the porcine muscle at quasi-static strain rates are very close to the data obtained from the indentation experiments on human forearm and lower limb soft tissues by Zheng et al. (1999). However, our data are stiffer than those obtained from quasi-static experiments on porcine fresh muscle tissues by Van Loocke et al. (2006b). This is perhaps because of different samples and testing conditions. Van Loocke et al. (2006b) used fresh muscles from a pelvic limb of 3-month-old male pigs for quasi-static experiments at
the strain rate of 0.0005 s1. However, our quasi-static experiments were conducted on the fresh muscles from a ham of a 5-month-old female pig at one and two orders of magnitudes higher strain rates. It should be noted that the testing conditions in the dynamic experiments conducted by Zheng et al. (1999) and Van Loocke et al. (2006a) are quite different from our constant high-rate experiments. This loading condition difference makes the direct comparison of resultant data inappropriate. Sligtenhorst et al. (2006) conducted high-rate testing of bovine muscle tissue by using the SHPB. Compared to their high-rate stress– strain data, the stress response for the porcine muscle tissue in this study is much lower. However, our data are very close to those for bovine muscle tissue, which was sliced perpendicular to the long axis of the bone, obtained by McElhaney (1966) over a strain rate ranging from 0.001 to 1000 s1. The stress response for the porcine muscle tissue is slightly lower than that for the bovine muscle tissue possibly because of different samples and sample conditions. Even though the similar loading devices are used, valid testing conditions are critical to obtain intrinsic material response. In this study, we employed modifications to the SHPB and specimen geometry to ensure valid testing conditions such that accurate stress–strain response for the porcine muscle tissue was obtained. Figs. 10 and 11 show the trends of stress versus strain rate at the engineering strain of 10%, 25%, and 45% along both directions in the porcine muscle tissue. The data for bovine muscle tissue by McElhaney are also plotted in both figures for comparison purposes. The strain-rate sensitivities for both the porcine muscle tissue and the bovine muscle tissue are observed to be consistent. Strain rate effects are apparent in the porcine muscle tissue studied in this research. The strain-rate dependency is clearly sensitive to the loading direction. The strain-rate sensitivity along the perpendicular direction is more significant than that along the fiber direction. The availability of stress–strain data for
Fig. 10. Strain rate effects of the porcine muscle along fiber direction.
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Fig. 11. Strain rate effects of the porcine muscle perpendicular to fiber direction.
the porcine muscle tissue over a wide range of strain rates is expected to make developing accurate strain-rate-dependent tissue models possible in the future. Acknowledgments This research was supported by US Army Research Laboratory (ARL) through a collaborative research agreement with Purdue University. The authors wish to thank Mr. Yi Pan and Mr. Chul Jin Syn for their efforts in the quasi-static experiments. References Butler, D.L., Goldstein, S.A., Guilak, F., 2000. Functional tissue engineering: the role of biomechanics. Transactions of the ASME, Journal of Biomechanical Engineering 122, 570–575. Casem, D., Weerasooriya, T., Moy, P., 2005. Inertia effects of quartz force transducers embedded in a split Hopkinson pressure bar. Experimental Mechanics 45, 368–376. Chen, W., Song, B., 2005. Dynamic compression testing on polymeric foams. In: Experiments in Automotive Engineering—Optical Techniques, 2005 SAE World Congress, April 11–14, 2005, Detroit, MI, USA. Chen, W., Zhang, B., Forrestal, M.J., 1999. A split Hopkinson bar technique for low-impedance materials. Experimental Mechanics 39, 81–85. Chen, W., Lu, F., Zhou, B., 2000. A quartz-crystal-embedded split Hopkinson pressure bar for soft materials. Experimental Mechanics 40, 1–6. Chen, W., Lu, F., Frew, D.J., Forrestal, M.J., 2002. Dynamic compression testing of soft materials. Transactions of the ASME, Journal of Applied Mechanics 69, 214–223. Davies, E., Hunter, S.C., 1963. The dynamic compression testing of solids by the method of the split Hopkinson pressure bar. Journal of the Mechanics and Physics of Solids 11, 155–179. Forrestal, M.J., Wright, T.W., Chen, W., 2007. The effect of radial inertia on brittle samples during the split Hopkinson pressure bar test. International Journal of Impact Engineering 34, 405–411.
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