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Basic Science

Electrical Conductivity of Lumbar Anulus Fibrosis: Effects of Porosity and Fixed Charge Density

Yong Gu, Wei, PhD; Justiz, Marc-Antoine, MSc; Yao, Hai, PhD

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The intervertebral disc (IVD), the largest avascular structure in the human body, is a charged hydrated soft tissue exhibiting mechano-to-electrical transduction phenomena, such as steaming potential. 16 The streaming potential is related to the electrochemical, electrical, and mechanical properties of a material (e.g., fixed charge density, hydraulic permeability, modulus, and electrical conductivity). 7–9,11,12,15,20,29,32 Numerous studies have been done on the biomechanical properties of IVD in order to understand the etiology of disc failure and related spine disorders. 40 However, little has been done on the electrical properties of IVD tissues. 16,18,24 The goal of the present study was to investigate the effects of varying tissue composition and structure on the electrical conductivity of lumbar anulus fibrosis (AF).

The normal AF consists of a series of concentric lamellae with a highly organized structure of collagen fiber bundles. 21,31 Water, proteoglycan (PG), and collagen are the major components of the tissue. 26,38 The fixed charges on the glycosaminoglycan chains of PGs are responsible for the electromechanical transduction phenomena observed in cartilaginous tissues. 11,12,16,27–29,32,33 Variations in tissue composition and structure in AF with degeneration will alter not only the mechanical properties but also the electrical properties of the AF.

The specific electrical conductivity (χ) is one of the material properties of a biologic tissue, determined by χ = h/rA where r is the electrical resistance measured across the height (h) of the specimen and A is the cross-sectional area of the specimen. The value of specific conductivity of cartilaginous tissues depends on the ion diffusivities and ion concentrations within the tissue. 4,6,10,11,15,19,20,32 It also depends on the pH value and the flow condition of bulk fluid. 4,6–8,10,11,15,19,20,32 In this study, the electrical conductivity of AF specimens was measured under zero fluid flow conditions. It is hypothesized that the specific conductivity of AF is sensitive to tissue porosity (i.e., volume fraction of water or water content) rather than fixed charge density (FCD) of AF in normal (physiologic) saline. To test this hypothesis in the present study, the specific conductivities of normal and enzyme-treated AF specimens were measured and correlated to tissue porosity using a recently developed technique. 18 Because the electrical conductivity is related to the streaming potential phenomenon and also depends on ion diffusivities, the present study is important for understanding electrical behavior and ion transport in the IVD.

Materials and Methods

Specimen Preparation.

Six lumbar discs were harvested from two Yorkshire domestic pigs (77 kg, L1–L2, and 85 kg, L1–L6) obtained from a local slaughterhouse within three hours of sacrifice. A total of 35 cylindrical plugs were punched axially from all regions of the AF of each disc using a 5-mm stainless steel corneal trephine. The plugs were cut while the IVDs were frozen to ensure a uniform cylinder diameter. Each plug was prepared to yield a disc-shaped specimen with parallel surfaces, top and bottom, using a sledge microtome (Model SM2400, Leica Instruments, Nussloch, Germany) with freezing stage (Model BFS-30, Physitemp Instruments Inc., Clifton, NJ). The procedure for specimen preparation is similar to those published in literature. 1,16,17,22 The thickness of the specimen was measured using a custom-designed current-sensing digital micrometer (3 μm precision). Ten specimens were used as the control group when comparing to 25 specimens treated with the trypsin enzyme (see below). Control and trypsin-treated specimens were taken from neighboring locations on the AF. The mean thickness of the specimens is listed in Table 1.

Table 1
Table 1:
Mean and Standard Deviation of Tissue Thickness, Porosity (Volume Fraction of Water), and Wet and Dry Tissue Densities for Control and Treated AF Specimens

Conductivity Apparatus.

An apparatus and technique for measuring conductivity of hydrated soft tissues under the condition of zero fluid flow (no convection) were recently developed for this investigation. 18,24 Briefly, the apparatus consisted of two stainless steel current electrodes, two Ag/AgCl voltage-sensing electrodes, a specimen chamber, a Keithley Source-meter, and a current-sensing digital micrometer (for height measurement) (Figure 1). The apparatus was calibrated using a conductivity standard in the range of 0.15–0.59 cm and found to be accurate (less than 5% nonlinearity) in the range of 0.22–0.59 cm. 18 A testing protocol for AF specimens was developed in the pilot study 18 and was adopted in the present study. Using the four-wire method, the conductivity of specimens was measured with constant direct current of 3 μA (density: 0.015 mA/cm2) at room temperature (22 ± 1 C). Our pilot studies demonstrated that the measurements were highly repeatable for AF specimens. 18

Figure 1
Figure 1:
Schematic of apparatus for measuring electrical conductivity, consisting of two stainless steel current electrodes, two Ag/AgCl voltage-sensing electrodes, a nonconductive plexiglass chamber, a current sensing micrometer, and a Keithley Source-meter (Model 2400).

One-Dimensional Free Swelling.

For the control group (n = 10), each of the specimens was allowed to swell axially in the conductivity apparatus for 10 minutes, while immersed in phosphate-buffered saline solution (PBS, pH 7.4) at room temperature (22 ± 1 C). The variations of specimen height and electrical conductivity were recorded over time. After 10 minutes, to facilitate water diffusion and swelling, the specimen was transferred to a 5-mm confining ring with porous walls and immersed in PBS. The ring allowed axial swelling of the specimen through axial and radial imbibition of solution while maintaining radial confinement. After a few minutes, the specimen was transferred to the conductivity apparatus for measurement of height and electrical conductivity. After the measurement (which took about 1 minute), the specimen was placed back into the confining ring for swelling until the next measurement. Care was taken to handle the specimens gently during specimen transfer to minimize changes in specimen hydration. This process continued for about 45 minutes (swelling time) until the specimen showed no significant increase in volume. The total testing process for each specimen took less than 90 minutes.

Trypsin Treatment.

For the treated group (n = 25), each of specimens was immersed in PBS containing 372 U/mL (0.04 mg/mL) trypsin (Sigma Chemical Co., Sigma Aldrich Corp., St. Louis, MO) at room temperature (22 ± 1 C) for 45 minutes. A separate study has shown that the above treatment protocol would significantly reduce the free-swelling strain, swelling pressure and equilibrium, and dynamic stiffness of AF specimens, 41 mainly due to the reduction in fixed charge density caused by proteoglycan depletion. 9,33 It was estimated that the treatment protocol would reduce tissue fixed charge density by 46%, based on the swelling pressure data measured for control and treated specimens. 41 After treatment, specimens were thoroughly rinsed in PBS and electrical conductivity was measured.

Porosity and Density Determinations.

Porosity is defined as the ratio of water volume to wet tissue volume. It is an alternative way to express tissue water content, which is slightly different in value from that more commonly reported in literature (i.e., water weight/wet tissue weight). 13,14,23 For the control group (n = 10), each of the specimens was weighed in air (wet weight, in grams) and in PBS before swelling. The initial specimen volume was calculated by dividing the difference between wet weight and weight in PBS by the mass density of PBS (Archimedes’ principle). Our pilot study has shown that this method for determining specimen volume is more accurate than direct calculation by assuming the specimen to be a perfect cylinder. During swelling, the specimen volume increased over time due to fluid imbibition. This volume increase was estimated by AΔh, where A is the cross-sectional area of the specimen, and Δh is the increase in specimen height measured by the conductivity apparatus. The increase in specimen wet weight was estimated by AΔhρpbspbs is mass density of PBS, 1.005 g/mL). For the treated group (n = 25), the specimen wet weight and weight in PBS were measured after trypsin treatment. Following electrical conductivity measurement, specimens were lyophilized to obtain their dry weights. The tissue porosity (volume fraction of water), wet tissue density (wet weight per wet tissue volume), and dry tissue density (dry weight per dry tissue volume) were determined using a method developed previously. 13,14


Effect of Trypsin Treatment and Swelling

The mean value and standard deviation (SD) of electrical conductivity of the control specimens were 5.60 ± 0.89 mS/cm (n = 10) before swelling and 9.11 ± 0.90 mS/cm (n = 10) after swelling in PBS. The difference was statistically significant (t test, P < 0.05;Figure 2). The electrical conductivity of trypsin-treated specimens was 7.92 ± 0.84 mS/cm (mean ± SD, n = 25). The difference in electrical conductivity between control specimens (after swelling in PBS for about 45 minutes) and treated specimens (i.e., swelling in trypsin solution for the same period of time) was statistically significant (t test, P < 0.05). The porosity (volume fraction of water) and dry tissue density for the control and treated groups are listed in Table 1. The trypsin treatment did not affect the dry tissue density of AF specimens (Table 1), suggesting that the collagen content of the tissue might not be altered by treatment. 14,23 However, the treatment significantly decreased the porosity of the specimens by 3.75% (t test, P < 0.05) relative to the porosity of control specimens (after swelling). The trend for porosity and density results is similar to that seen for bovine articular cartilage. 14,23

Figure 2
Figure 2:
Mean and standard deviation of specific electrical conductivity for the control group before and after swelling, and for trypsin-treated group (after swelling).

The value of specific conductivity for AF measured in the present study was similar to the values for human and bovine articular cartilage. 4,6,10,11,19,32

Correlation Between Electrical Conductivity and Porosity

For the control specimens, there existed a significant, linear correlation between electrical conductivity and porosity (R2 = 0.87;P < 0.0001 for 86 points from 10 different specimens, see Figure 3). The linear correlation may be described by the trend line equation: χ = 37.68φw − 22.19, where χ is the specific conductivity (mS/cm), and φw is the porosity of the specimen. This equation predicts that the specific conductivity would approach a value of 15.49 mS/cm for the tissue with 100% porosityw = 1.0). This is very close to the value (15.53 mS/cm) for the PBS solution that was used to hydrate the tissue, measured by a conductivity meter (Model 150Aplus, Orion, Orion Research Inc., Boston, MA) at room temperature, 23 C. Thus, the correlation of conductivity with porosity may be expressed by the following empirical equation 2,37: where χo is the conductivity of PBS, and α is the dimensionless parameter. For the control specimens, α = 2.43 for χo = 15.49 mS/cm at room temperature (22C); see Figure 3. Equation (1) was also used to curve-fit conductivity data for treated specimens (Figure 3)and yielded α = 2.46 (R2 = 0.37). From Figure 3, one can see that the trypsin treatment did not significantly change the conductivity of treated specimens compared to control specimens of similar tissue porosity.

Figure 3
Figure 3:
Linear correlation of specific conductivity with tissue porosity for control (86 measurements) and trypsin-treated (n = 25) AF specimens in PBS at room temperature (22 C). For control specimens, the best fit is χ = 37.68φw − 22.19 (mS/cm), or χ = χo[1 − 2.43(1 − φw)] with χo = 15.49 mS/cm (R2 = 0.87). For treated specimens, the best fit is χ = χo[1 − 2.46 (1 − φw)] with χo = 15.49 mS/cm (R2 = 0.37). Specific conductivity values for treated specimens do not differ significantly from those for control specimens with similar porosity.


The objective of the present study is to investigate the effect of tissue composition on the electrical properties of IVD tissue. More specifically, we focus on the influence of tissue porosity and fixed charge density on the value of specific conductivity. It is known that the value of conductivity of a tissue with fluid flow is in general greater than that without fluid flow. 4,6–8,10,11,15,19,20,32 In the present study, the electrical conductivity of AF specimens was measured under zero fluid flow condition. Under this condition, the measured specific conductivity (χ) is given by (for the simplicity of discussion, we consider major ions in the tissue, i.e., Na+ and Cl only):EQUATION

where Fc is the Faraday constant, φw is the tissue porosity, c+ and c are the Na+ and Cl ion concentrations, respectively (per volume of tissue fluid), D+ and D are the Na+ and Cl ion diffusivities within the tissue, respectively, R is the gas constant, and T is the absolute temperature. 10,12,19,20,25,32 The cation (Na+) concentration and anion (Cl) concentration is related through the electroneutrality condition: c+ = c + cF, where cF is the absolute value of the fixed charge density. Thus, the electrical conductivity is related to the tissue fixed charge density.

It is known that the ion diffusivities increase with increasing tissue porosity. 30,32,34–36 The trypsin treatment reduces not only the fixed charge density, 9,33 but also the tissue porosity (Table 1) and swelling pressure compared to the control specimens (after swelling). 41 The decrease in conductivity for treated specimens compared to control specimens after swelling is mainly due to the decrease in ion diffusivities resulting from reduced tissue porosity (Figure 2). This is evidenced by the results demonstrating that specific conductivity for treated specimens is similar to that for the control specimens with similar porosity (Figure 3). Our pilot study has shown that the swelling behavior and mechanical properties of the control specimens were significantly different from those of the treated specimens, 41 indicating differences in fixed charge density. Thus, the measured conductivity for AF specimens in PBS is mainly determined by tissue porosity, rather than fixed charge density, provided that there is no change in tissue collagen structure. This insensitivity to fixed charge density in normal saline was also found for articular cartilage. 19

This argument is further supported by the data for the control specimens (Figure 3). During the swelling of AF specimens in PBS, although fixed charged density decreases, the average value of conductivity increased by 63% as average tissue porosity increased by 12% after swelling (Figure 2 and Table 1). This, again, may be attributed to an increase in ion diffusivities with porosity, 10,30,32,34–36 because a decrease in fixed charge density would not have significant effect on the value of conductivity of AF in physiologic saline, as demonstrated by our data for trypsin-treated AF specimens (Figure 3) and by the data for cartilage. 19

The linear correlation of conductivity with tissue porosity for AF specimens was similar to the electrical conductivity behavior of protein solutions measured at 1 kHz 2 and of other hydrated tissues (brain, liver, skeletal muscle, etc.) measured at 100 MHz, 37 but not similar to that of cartilage reported as strain-dependent conductivity. 3

The water content of AF decreases with disc degeneration or aging. 17,38,39 Our data suggest that the rate of ion transport in AF would decrease with degeneration or aging. This may affect tissue nutrition. The conductivity measurement together with empirical equation (1) may be used for detecting changes in tissue porosity (hydration) when assessing disc degeneration. Note that this empirical equation is valid only for specimens with high porosity (>∼60%), because the value of conductivity cannot be negative for low hydration tissues.

Changes in structure and composition of AF will influence its value of specific conductivity because ion diffusivities are a function of tissue composition and structure. Thus, the electrical conductivity is expected to vary with disc level and the region within the disc. There is evidence that the specific conductivity of normal AF is anisotropic because the hydraulic permeability and streaming potential are both anisotropic. 16,17 Both of these were not investigated in this study. Other sources of error or limitations of the study include the small number of animals used and the lack of direct measurement of fixed charge density. Nonetheless, the present study did provide useful information on the effect of water content on electrical property of IVD tissues.


Electrical conductivity and porosity (volume fraction of water) of normal and trypsin-treated porcine lumbar AF specimens in PBS were measured. The effects of tissue porosity and fixed charge density on conductivity were investigated. Tissue porosity plays a dominant role in the measured conductivity. There is a significant linear correlation between electric conductivity and porosity for control AF specimens. The mean value of specific conductivity for trypsin-treated specimens was smaller than that for control specimens because the treated specimens had lower water content. Results for both control and treated specimens show that electrical conductivity is sensitive to tissue porosity, but not to tissue fixed charge density for porcine AF specimens in PBS.

Key Points:

  • Electrical conductivity is linearly correlated with water content for lumbar anulus fibrosis tested.
  • Electrical conductivity is insensitive to fixed charge density for anulus fibrosis equilibrated in PBS.
  • Results are useful for understanding the electrical behavior and ion diffusion in normal and degenerated IVD tissues.


The authors wish to thank D. Flagler for his technical support.


1. Best BA, Guilak F, Setton LA, et al. Compressive mechanical properties of the human anulus fibrosus and their relationship to biochemical composition. Spine 1994; 19: 212–21.
2. Bull HB, Breese K. Electrical conductance of protein solutions. J Colloid Interface Sci 1969; 29: 492–95.
3. Chammas P. Electromechanical coupling in articular cartilage: an electromechanical micromodel and experimental results [master’s thesis]. Boston, MA: Boston University; 1989.
4. Chammas P, Federspiel WJ, Eisenberg SR. A microcontinuum model of electrokinetic coupling in the extracellular matrix: pertubation formulation and solution. J Colloid Interface Sci 1994; 168: 526–38.
Chen AC, Nguyen TT, Sah RL. Streaming potential during the confined compression creep test of normal and proteoglycan-depleted cartilage. Ann Biomed Eng 1997; 25: 269–77.
6. Eisenberg SR, Grodzinsky AJ. Electrokinetic micromodel of extracellular-matrix and other polyelectrolyte networks. Physicochem Hydrodynamics 1988; 10: 517–39.
7. Frank EH, Grodzinsky AJ. Cartilage electromechanics—I. Electrokinetic transduction and the effects of electrolyte pH and ionic strength. J Biomech 1987; 20: 615–27.
8. Frank EH, Grodzinsky AJ. Cartilage electromechanics—II. A continuum model of cartilage electrokinetics and correlation with experiments. J Biomech 1987; 20: 629–39.
9. Frank EH, Grodzinsky AJ, Koob TJ, et al. Streaming potentials: A sensitive index of enzymatic degeneration in articular cartilage. J Orthop Res 1987; 5: 497–508.
10. Frank EH, Grodzinsky AJ, Phillips SL, Grimshaw PE. In: Mow VC, Ratcliffe A, Woo SL-Y (eds). Biomechanics of Diarthrodial Joints. New York, NY: Springer-Verlag; 1990:261–82.
11. Grodzinsky AJ. Electromechanical and physical properties of connective tissue. Crit Rev Biomed Eng 1983; 9: 133–99.
12. Gu WY, Lai WM, Mow VC. Transport of fluid and ions through a porous-permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage. J Biomech 1993; 26: 709–23.
13. Gu W, Lewis B, Lai WM, et al. A technique for measuring volume and true density of the solid matrix of cartilaginous tissues. ASME Adv Bioeng 1996; 33: 89–90.
14. Gu WY, Lewis B, Saed-Nejad F, et al. Hydration and true density of normal and PG-depleted bovine articular cartilage. Trans Orthop Res Soc 1997; 22: 826.
15. Gu WY, Lai WM, Mow VC. A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors. J Biomech Eng 1998; 120: 169–80.
16. Gu WY, Mao XG, Rawlins BA, et al. Streaming potential of human lumbar anulus fibrosus is anisotropic and affected by disc degeneration. J Biomech 1999; 32: 1183–89.
17. Gu WY, Mao XG, Foster RJ, et al. The anisotropic hydraulic permeability of human lumbar anulus fibrosus: influence of age, degeneration, direction, and water content. Spine 1999; 24: 2449–55.
18. Gu WY, Justiz MA. Apparatus for measuring the swelling dependent electrical conductivity of charged hydrated soft tissues. J Biomech Eng. In press.
19. Hasegawa I, Kuriki S, Matsuno S, et al. Dependence of electrical conductivity on fixed charge density in articular cartilage. Clin Orthop Res 1983; 177: 283–88.
20. Helfferich F. Ion Exchange. New York, NY: McGraw Hill; 1962.
21. Hickey DS, Hukins DWL. Relation between the structure of the anulus fibrosus and the function and failure of the intervertebral disc. Spine 1980; 5: 106–16.
22. Iatridis JC, Setton LA, Foster RJ, et al. Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. J Biomech 1998; 31: 535–44.
23. Joseph D, Gu WY, Mao XG, et al. True density of normal and enzymatically treated bovine articular cartilage. Trans Orthop Res Soc 1999; 24: 642.
24. Justiz AM, Cheung H, Gu WY. Electrical conductivity of annulus fibrosis. Trans Orthop Res Soc 2001; 26: 883.
25. Katchalsky A, Curran PF. Nonequilibrium Thermodynamics in Biophysics. 4th printing. Cambridge, MA: Harvard University Press; 1975.
26. Kraemer JD, Kolditz M, Gowin R. Water and electrolyte content of human intervertebral discs under variable load. Spine 1985; 10: 69–71.
27. Lai WM, Hou JS, Mow VC. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J Biomech Eng 1991; 113: 245–58.
28. Lai WM, Mow VC, Sun DD, et al. On the electric potentials inside a charged soft hydrated biological tissue: streaming potential versus diffusion potential. J Biomech Eng 2000; 122: 336–46.
29. Lee RC, Frank EH, Grodzinsky EH, et al. Oscillatory compressional behavior of articular cartilage and its associated electromechanical properties. J Biomech Eng 1981; 103: 280–92.
30. Mackie JS, Meares P. The diffusion of electrolytes in a cation-exchange resin. I. Theoretical. Proc R Soc London 1955; A232: 498–509.
31. Marchand F, Ahmed AM. Investigation of the laminate structure of lumbar disc anulus fibrosus. Spine 1990; 15: 402–10.
32. Maroudas A. Physico-chemical properties of cartilage in the light of ion exchange theory. Biophys J 1968; 8: 575–95.
33. Maroudas A, Muir AH, Wingham J. The correlation of fixed negative charge with glycosaminoglycan content of human articular cartilage. Biochem Biophys Acta 1969; 177: 492–500.
34. Maroudas A, Weinberg PD, Parker KH, et al. The distributions and diffusivities of small ions in chondroitin sulphate, hyaluronate and some proteoglycan solutions. Biophys Chem 1988; 32: 257–70.
35. Ogston AG, Preston BN, Wells JD. On the transport of compact particles through solutions of chain-polymers. Proc R Soc London 1973; A333: 297–316.
36. Parker KH, Winlove CP, Maroudas A. The theoretical distributions and diffusivities of small ions in chondroitin sulphate and hyaluronate. Biophys Chem 1988; 32: 271–82.
37. Schepps JL, Foster KR. The UHF and microwave dielectric properties of normal and tumour tissues: variation in dielectric properties with tissue water content. Phys Med Biol 1980; 25: 1149–59.
38. Urban J, Maroudas A. The chemistry of the intervertebral disc in relation to its physiological function and requirements. Clin Rheumatic Dis 1980; 6: 51–77.
39. Urban JPG, McMullin JF. Swelling pressure of the lumbar intervertebral discs: Influence of age, spinal level, composition, and degeneration. Spine 1988; 13: 179–87.
40. Weinstein JN, Gordon SL. Low Back Pain: A Scientific and Clinical Overview. Rosemont, IL: American Academy of Orthopaedic Surgeons; 1996.
41. Yao H, Justiz MA, Flagler D, et al. Dynamic behavior of normal and trypsin-treated lumbar annulus fibrosis in confined compression: effects of swelling pressure and hydraulic permeability. Ann Biomed Eng. In review.

intervertebral disc; anulus fibrosis; electrical conductivity; porosity; water content; fixed charge density; spine]Spine 2002;27:2390–2395

© 2002 Lippincott Williams & Wilkins, Inc.