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Stress-strain relationship of the spinal cord of anesthetized cats
J Bmnwchrrmcs Vol 14. No 4. pp 269-276. 1981 PrInted in Great Bnmn
TECHNICAL
STRESS-STRAIN
NOTE
RELATIONSHIP OF THE SPINAL CORD OF ANESTHETIZED CATS*
Abstract-An in oioo experimental method was developed to measure the mechanical or rheological properties of the spinal cord of anesthetized cats. This novel approach resulted in the measurements of the tensile force in the cord and the modulus of the spinal cord tissue under longitudinal elongation.
INTRODUCTION Insight into the biomechanical factors involved in the spinal cord injury is of importance to the understanding of physiopathological development of lesion, clinical treatment and therapy. Prior to 1975, the only mechanical data associated with an irreversible impact injury to the spinal cord of cats, dogs or monkeys were the drop of a 20 g mass from a 20 cm height onto an exposed cord through laminectomy (Allen, 1911; White and Albin, 1970). The impact force and deformation associated with such an open injury model were reported by Hung et al. (1975, 1979a) and Dohrmarm and Panjabi (1976). To compute the spinal cord deformation during impact (Hung er al., 1979b). one has to know the material properties of the spinal cord. In this paper, a novel in viuo experiment was developed to measure the stress-strain relationship of the spinal cord of anesthetized cats.
EXPERIMENTAL
PROCEDURE
Cats were anesthetized with i.v. sodium pentobarbital under controlled ventilation. The cat was placed horizontally and the spinal column between T4 and L4 was supported and immobilizedt by a specially designed frame with four straight rods or nails on each side. The rigid frame had a fixed base with two pairs of the aforementioned rods. The other two pairs were mounted on a sliding base which could be adjusted to control the distance (at a precision of 0.03 mm) between these two pairs of rods and the former two sets (refer to Fig. 1). This design enabled us to measure the tensile force existing in the spinal cord of an anesthetized cat. Laminectomy was performed in the middle thoracic and upper lumbar regions (i.e. from T6 to L3). Portions of the anterior column and the dura mater (from T8 to Ll) were also removed for the in uioo measurement of the longitudinal stress-strain relationship of the spinal cord (Fig. 2). The cat was then positioned vertically onto an Instron Universal Testing Machine. Two small rings which were solely sup ported by a fixed frame and the Instron load cell, respectively, were glued onto the cord using a very thin coating of super glue or dental glue, applied only on the inner surface of these rings. The effect of such a thin coating on the stress-strain relationship was believed to be relatively insignificant in the present study. The clearance between these two rings was set initially at 25 mm. Each ring was made of two half-ellipses. The weight of the ring attached to the Instron load cell was
* Received 23 April 1980. t The spinal column between T4 and L4 was kept straight without stretching. 269
checked by the recording system. A slight relaxation of the straight spinal column was made by adjusting the aforementioned sliding base, resulting in the transfer of the existing tensile force, FO, in the cord to these two rings and to the Instron load cell. This procedure yielded a direct measurement of the tensile force in the cord. The sliding base was readjusted to return to its original position at a similar slow rate so that the tensile force was supported by the spinal column again. Thus, the longitudinal tension on the ring reduced to zero. The third ring was then glued onto the cord. Its weight was supported by the Instron crosshead, but not by the load cell. After attaching this ring at a short distance (about 8 mm) above the ring which was connected to the load cell for force measurement, we were in a position to conduct uniaxial tension experiments of the spinal cord by displacing these two rings at the same rate while keeping the bottom one stationary (Fig. 3). In order to prevent the moisture problem, the test section of the exposed spinal cord was housed in a smalllucitecontainer, assembled by two half-cylindrical cups. and filled with Normosal as a CSF (cerebrospinal fluid) substitute. The temperature of the fluid was adjusted to 37~C. Except for the times of the attaching of these three rmgs onto thecord, the cord was frequently sprayed with the Normosol. The mechanical properties of the cord would otherwise have been altered within 2 min. Simultaneous recordings of the force and strain between the lower two rings were obtained when the cord segment was stretched continuously and returned to its original length (25 mm long) by the Instron Machine at a very slow rate of 1.25mm/min. The load cell was sensitive to 60 dynes minimum and 200,COO dynes maximum. No shppage occurred between the rings and the spinal cord unless the elongation exceeded 5O”/b.Because of the slippage of the rmgs from the spinal cord at a larger strain, we encountered experimental difficulties in a determination of the threshold elongation associated with an irreversible Injury to the spinal cord. In the recent chronic animal experiments. no infection or tissue degeneration was visually observed 2 weeks after the rings were glued onto the cord by super glue or dental glue.
RESULTS
AND
DISCUSSIONS
The stress-strain relationship of the spmal cord with the dural sheath removed under a quasi-static uniaxial (or longitudinal) tension was measured for several anesthetized cats. The tension was applied under a constant strain rate of 0.02 min-‘. Figure 4 shows the salient linear and non-linear regions of the spinal cord tissue under axial elongation along with a strong hysteresis during the gradual unloadmg phase
Technical
270
0
2
4
Note
6
6
10
12
stror O/o Fig. 4.
c
0
CAT
z
4
6
8
Strom % Fig. 5
Fig. 6.
IO
3~
!z
274
Fig. 8.
Technical (i.e. reduction of elongation at the same strain rate). The tensile force F, exerted on the cord in the natural state was found to vary between 4000 and 6000 dynes. Such a deviation appeared to be relatively small and might be affected by immobilization of the spinal column onto the rigid frame. In Fig. 4, the data for cats 1 and 2 are about the same. There are some disagreements between these data and those for cats 3 and 4. The latter two were subjected to higher strain prior to the gradual reduction of the strain. The present data also showed some plastic behavior of the cord - the presence of a residual strain when the loading returned to its initial value. Also, there was a small drop in force or stress (in comparison with the initial tension) when the strain was reduced to zero. The results in Fig. 4 were replotted in terms of stress-strain relationship in Fig. 5. Here, the initial prestress was adjusted graphically to the same value (2 x lo4 dyn/cm*). The slopes of the curves in Fig. 5 represent the moduli of the spinal cord during gradual elongation. The solid line and the data point in Fig. 6 show the variation of the modulus for cat I during the complete cycle of longitudinal deformation. The former was based on a constant cross-sectional area A(= 0.25 nab) calculated from the measured lateral dimension a (the major diameter) and the anterior-posterior dimension b (the minor diameter) of an undeformed spinal cord with an assumption of elliptical shape. The deviation of the assumed elliptical cross-sectional area with the actual one was estimated to be
Note
275
about 5%. A constant modulus of 4 x IO6 dyn/cm2 was obtained for strain less than SP/,. The data points shown in Fig. 6 indicate the change in the modulus calculated from the cross-sectional area of the mid-section which was assumed to remain an elliptical shape, but with a parabolic decrease in the cord dimensions from the fixed values of a and bon either end as the spinal cord tissue was glued onto two rigid rings. A pronounced decrease in the modulus was seen when the strain was continuously or gradually increased beyond 6%. This trend was opposite to the isolated specimens of cadaver reported by Breig (1960). The present results and those of Breig represented the “combined” modulus of the cord substance and the pia mater. The high moduli of Breig’s results of cadaver - 4 to 16 times larger than our data of anesthetized cats-reflected the drastic changes in rheological properties of the spinal cord in in oitro situations. Also shown in Fig. 6 is a sharp increase in the modulus of the strain when the strain rate is reversed. The discontinuity in the modulus curve (tangential modulus) is solely due to the sudden change in strain rate - from positive to negative. During the period of the reduction ofelongation, the modulus reduced rapidly and became much smaller than the original value of 4 x lo6 dyn/cm’. Three of the four experiments reported in Fig. 4 were subjected to two similar repeated loadings. The time interval between every two uniaxial loadings was about 5 min which
CAT 2
Fig. 7
276
Technical
Note
Fig. 9
might not have been long enough for a full recovery of the mechanical properties of the spinal cord tissue. As shown in Fig. 7, the linear regions for the second and third loadings are much smaller than that for the first one. A marked reduction in the modulus (as represented by the relatively milder slopes of stress-strain curves) can be seen, initially in these repeated uniaxial loadings. The nonlinear viscoelastic behavior is reflected in the pronounced effects of strain (or loading) history on the stress-strain relationship (Hung et al., 1979b). Recently, we have made several improvements in the in oiuo measurements of the stress-strain relattonship of the spinal cord of cats. The region of laminectomy was reduced from T&L3 to Ll-L2. No spinal cord root was dissected for the latter. The lucite rings were replaced by stainless steel rings (refer to Fig. 8). Each ring was made of two half-ellipses of a sickle-shape. The width of the ring was 2.5 mm instead of 5 mm for the lucite ring. Two rings were glued onto the pia mater of the spinal cord at Ll with a spacing of 559 mm. The third ring was attached onto L2. The dissected skin of the animal was stretched and sutured to form a bag supported by a rigid frame which was not in contact with the rings. The skin-bag was then filled with Normosol heated at 37’C. Figure 9 shows the results of two cat experiments. one with the maximum stratn of l”,, and the other 1.6”,. The pseudo Young’s modulus was found to be 2.5 x lo6 dyn/cm’ Instead of4 x lo6 dynicm’ shown in Figs. 5 and 6. The higher value for the latter was atrributed to the effects of the dissection of several pairs of spinal cord roots. In a series of I7 cat experiments. the mean pseudo Young’s modulus was found to be 2.6 x 10” dynicm’ (with a variation of kO.3 x lo6 dyn/cm’). This value was about one-sixth of the in citro data ofcadaver reported by Breig in 1960. In his longitudmal tension experiments. the spinal cord segment (about 9.2 cm long) was dissected and suspended in au Calculating from his experimental data, one can obtain a modulus of 17.2 x lOh dyn/cm’ for a 29; strain and over 50 x IO6 dyn/cm’ for 3”“. Such large moduli were entirely caused by the tncrease in dryness of the spinal cord specimen when exposed to air. This artifact was identified recently in a similar in uitro puppy experiment in our laboratory (Hung and Chang, 1981). It should be mentioned that Breig concluded that “the results could not be extended to the forces actmg in the cord in situ”. The success of the improved in uivo experiments (with the spinal cord roots intact) will lead us to study the threshold of
spinal cord under longitudinal elongation and to determme the viscoelastic properties of the spinal cord. Acknowledgements
The study was supported by the National Institute of Neurological and Communicative Disorders and Stroke, NIH. under Grant 5-ROl-NS-13238.
REFERENCES Allen, A. R. (1911) Surgery of experimental lesion of spinal cord equivalent to crush injury of fracture dislocation of spinal column. J. Am. med. Ass. S-7, 878-880. Breig, A. (1960) Biomechanics ofrhe Cenrral Nervous System Almquist & Wiksell, Stockholm. Dohrmann, G. J. and Panjab, M. M. (1976) Standardized spinal cord trauma: biomechanical parameters and lesion volume. Surg. Neural. 6, 263-267. Hung, T. K., Albin, M. S., Brown, T. D., Bunegin, L., Albin, R. and Jannetta, P. J. (1975) Biomechanical responses to open experimental spinal cord injury. Surg. Neural. 4, 271-276. Hung,T. K., Lin, H. S.,Albin, M. S., Bunegin, L. and Jannetta, P. J. (1979a) The standardization of experimental impact injury to the spinal cord. Surg. Neural. 11, 470-477. Hung, T. K., Chang, G. L., Lin, H. S., Chang, J. L. and Feng, W. W. (1979b). Biorheology and experimental trauma of spinal cord of cats. Proc. Third ASCE Engng Mech. DII Speciality Coflj Hung, T. K. and Chang, G. L. (1981). Biomechanical and neurological responses of the spinal cord of puppy to uniaxial tensions. J. biomed. Engng. ASMG (in press). White, R. J. and Albin, M. S. (1970) Spine and spinal cord injury. In Impact Injury and Crash Protection (Edited by Gurdjian, E. S., Lange, W. A., Patrick, L. M. and Thomas L. M. pp. 63-84. Charles C. Thomas, Springfield, Illinois.
Department
of Neurological
Surgery and Department of Civil Engineering, University of Pittsburgh. Pittsburgh. PA 15261, U .S.A
TIN-KAN HL~(; GUAN-LIANG CHAN(, HSIN-SL.N LI\ FRAW R. WAI.TLR LEON BLX=+~;I\
TECHNICAL
STRESS-STRAIN
NOTE
RELATIONSHIP OF THE SPINAL CORD OF ANESTHETIZED CATS*
Abstract-An in oioo experimental method was developed to measure the mechanical or rheological properties of the spinal cord of anesthetized cats. This novel approach resulted in the measurements of the tensile force in the cord and the modulus of the spinal cord tissue under longitudinal elongation.
INTRODUCTION Insight into the biomechanical factors involved in the spinal cord injury is of importance to the understanding of physiopathological development of lesion, clinical treatment and therapy. Prior to 1975, the only mechanical data associated with an irreversible impact injury to the spinal cord of cats, dogs or monkeys were the drop of a 20 g mass from a 20 cm height onto an exposed cord through laminectomy (Allen, 1911; White and Albin, 1970). The impact force and deformation associated with such an open injury model were reported by Hung et al. (1975, 1979a) and Dohrmarm and Panjabi (1976). To compute the spinal cord deformation during impact (Hung er al., 1979b). one has to know the material properties of the spinal cord. In this paper, a novel in viuo experiment was developed to measure the stress-strain relationship of the spinal cord of anesthetized cats.
EXPERIMENTAL
PROCEDURE
Cats were anesthetized with i.v. sodium pentobarbital under controlled ventilation. The cat was placed horizontally and the spinal column between T4 and L4 was supported and immobilizedt by a specially designed frame with four straight rods or nails on each side. The rigid frame had a fixed base with two pairs of the aforementioned rods. The other two pairs were mounted on a sliding base which could be adjusted to control the distance (at a precision of 0.03 mm) between these two pairs of rods and the former two sets (refer to Fig. 1). This design enabled us to measure the tensile force existing in the spinal cord of an anesthetized cat. Laminectomy was performed in the middle thoracic and upper lumbar regions (i.e. from T6 to L3). Portions of the anterior column and the dura mater (from T8 to Ll) were also removed for the in uioo measurement of the longitudinal stress-strain relationship of the spinal cord (Fig. 2). The cat was then positioned vertically onto an Instron Universal Testing Machine. Two small rings which were solely sup ported by a fixed frame and the Instron load cell, respectively, were glued onto the cord using a very thin coating of super glue or dental glue, applied only on the inner surface of these rings. The effect of such a thin coating on the stress-strain relationship was believed to be relatively insignificant in the present study. The clearance between these two rings was set initially at 25 mm. Each ring was made of two half-ellipses. The weight of the ring attached to the Instron load cell was
* Received 23 April 1980. t The spinal column between T4 and L4 was kept straight without stretching. 269
checked by the recording system. A slight relaxation of the straight spinal column was made by adjusting the aforementioned sliding base, resulting in the transfer of the existing tensile force, FO, in the cord to these two rings and to the Instron load cell. This procedure yielded a direct measurement of the tensile force in the cord. The sliding base was readjusted to return to its original position at a similar slow rate so that the tensile force was supported by the spinal column again. Thus, the longitudinal tension on the ring reduced to zero. The third ring was then glued onto the cord. Its weight was supported by the Instron crosshead, but not by the load cell. After attaching this ring at a short distance (about 8 mm) above the ring which was connected to the load cell for force measurement, we were in a position to conduct uniaxial tension experiments of the spinal cord by displacing these two rings at the same rate while keeping the bottom one stationary (Fig. 3). In order to prevent the moisture problem, the test section of the exposed spinal cord was housed in a smalllucitecontainer, assembled by two half-cylindrical cups. and filled with Normosal as a CSF (cerebrospinal fluid) substitute. The temperature of the fluid was adjusted to 37~C. Except for the times of the attaching of these three rmgs onto thecord, the cord was frequently sprayed with the Normosol. The mechanical properties of the cord would otherwise have been altered within 2 min. Simultaneous recordings of the force and strain between the lower two rings were obtained when the cord segment was stretched continuously and returned to its original length (25 mm long) by the Instron Machine at a very slow rate of 1.25mm/min. The load cell was sensitive to 60 dynes minimum and 200,COO dynes maximum. No shppage occurred between the rings and the spinal cord unless the elongation exceeded 5O”/b.Because of the slippage of the rmgs from the spinal cord at a larger strain, we encountered experimental difficulties in a determination of the threshold elongation associated with an irreversible Injury to the spinal cord. In the recent chronic animal experiments. no infection or tissue degeneration was visually observed 2 weeks after the rings were glued onto the cord by super glue or dental glue.
RESULTS
AND
DISCUSSIONS
The stress-strain relationship of the spmal cord with the dural sheath removed under a quasi-static uniaxial (or longitudinal) tension was measured for several anesthetized cats. The tension was applied under a constant strain rate of 0.02 min-‘. Figure 4 shows the salient linear and non-linear regions of the spinal cord tissue under axial elongation along with a strong hysteresis during the gradual unloadmg phase
Technical
270
0
2
4
Note
6
6
10
12
stror O/o Fig. 4.
c
0
CAT
z
4
6
8
Strom % Fig. 5
Fig. 6.
IO
3~
!z
274
Fig. 8.
Technical (i.e. reduction of elongation at the same strain rate). The tensile force F, exerted on the cord in the natural state was found to vary between 4000 and 6000 dynes. Such a deviation appeared to be relatively small and might be affected by immobilization of the spinal column onto the rigid frame. In Fig. 4, the data for cats 1 and 2 are about the same. There are some disagreements between these data and those for cats 3 and 4. The latter two were subjected to higher strain prior to the gradual reduction of the strain. The present data also showed some plastic behavior of the cord - the presence of a residual strain when the loading returned to its initial value. Also, there was a small drop in force or stress (in comparison with the initial tension) when the strain was reduced to zero. The results in Fig. 4 were replotted in terms of stress-strain relationship in Fig. 5. Here, the initial prestress was adjusted graphically to the same value (2 x lo4 dyn/cm*). The slopes of the curves in Fig. 5 represent the moduli of the spinal cord during gradual elongation. The solid line and the data point in Fig. 6 show the variation of the modulus for cat I during the complete cycle of longitudinal deformation. The former was based on a constant cross-sectional area A(= 0.25 nab) calculated from the measured lateral dimension a (the major diameter) and the anterior-posterior dimension b (the minor diameter) of an undeformed spinal cord with an assumption of elliptical shape. The deviation of the assumed elliptical cross-sectional area with the actual one was estimated to be
Note
275
about 5%. A constant modulus of 4 x IO6 dyn/cm2 was obtained for strain less than SP/,. The data points shown in Fig. 6 indicate the change in the modulus calculated from the cross-sectional area of the mid-section which was assumed to remain an elliptical shape, but with a parabolic decrease in the cord dimensions from the fixed values of a and bon either end as the spinal cord tissue was glued onto two rigid rings. A pronounced decrease in the modulus was seen when the strain was continuously or gradually increased beyond 6%. This trend was opposite to the isolated specimens of cadaver reported by Breig (1960). The present results and those of Breig represented the “combined” modulus of the cord substance and the pia mater. The high moduli of Breig’s results of cadaver - 4 to 16 times larger than our data of anesthetized cats-reflected the drastic changes in rheological properties of the spinal cord in in oitro situations. Also shown in Fig. 6 is a sharp increase in the modulus of the strain when the strain rate is reversed. The discontinuity in the modulus curve (tangential modulus) is solely due to the sudden change in strain rate - from positive to negative. During the period of the reduction ofelongation, the modulus reduced rapidly and became much smaller than the original value of 4 x lo6 dyn/cm’. Three of the four experiments reported in Fig. 4 were subjected to two similar repeated loadings. The time interval between every two uniaxial loadings was about 5 min which
CAT 2
Fig. 7
276
Technical
Note
Fig. 9
might not have been long enough for a full recovery of the mechanical properties of the spinal cord tissue. As shown in Fig. 7, the linear regions for the second and third loadings are much smaller than that for the first one. A marked reduction in the modulus (as represented by the relatively milder slopes of stress-strain curves) can be seen, initially in these repeated uniaxial loadings. The nonlinear viscoelastic behavior is reflected in the pronounced effects of strain (or loading) history on the stress-strain relationship (Hung et al., 1979b). Recently, we have made several improvements in the in oiuo measurements of the stress-strain relattonship of the spinal cord of cats. The region of laminectomy was reduced from T&L3 to Ll-L2. No spinal cord root was dissected for the latter. The lucite rings were replaced by stainless steel rings (refer to Fig. 8). Each ring was made of two half-ellipses of a sickle-shape. The width of the ring was 2.5 mm instead of 5 mm for the lucite ring. Two rings were glued onto the pia mater of the spinal cord at Ll with a spacing of 559 mm. The third ring was attached onto L2. The dissected skin of the animal was stretched and sutured to form a bag supported by a rigid frame which was not in contact with the rings. The skin-bag was then filled with Normosol heated at 37’C. Figure 9 shows the results of two cat experiments. one with the maximum stratn of l”,, and the other 1.6”,. The pseudo Young’s modulus was found to be 2.5 x lo6 dyn/cm’ Instead of4 x lo6 dynicm’ shown in Figs. 5 and 6. The higher value for the latter was atrributed to the effects of the dissection of several pairs of spinal cord roots. In a series of I7 cat experiments. the mean pseudo Young’s modulus was found to be 2.6 x 10” dynicm’ (with a variation of kO.3 x lo6 dyn/cm’). This value was about one-sixth of the in citro data ofcadaver reported by Breig in 1960. In his longitudmal tension experiments. the spinal cord segment (about 9.2 cm long) was dissected and suspended in au Calculating from his experimental data, one can obtain a modulus of 17.2 x lOh dyn/cm’ for a 29; strain and over 50 x IO6 dyn/cm’ for 3”“. Such large moduli were entirely caused by the tncrease in dryness of the spinal cord specimen when exposed to air. This artifact was identified recently in a similar in uitro puppy experiment in our laboratory (Hung and Chang, 1981). It should be mentioned that Breig concluded that “the results could not be extended to the forces actmg in the cord in situ”. The success of the improved in uivo experiments (with the spinal cord roots intact) will lead us to study the threshold of
spinal cord under longitudinal elongation and to determme the viscoelastic properties of the spinal cord. Acknowledgements
The study was supported by the National Institute of Neurological and Communicative Disorders and Stroke, NIH. under Grant 5-ROl-NS-13238.
REFERENCES Allen, A. R. (1911) Surgery of experimental lesion of spinal cord equivalent to crush injury of fracture dislocation of spinal column. J. Am. med. Ass. S-7, 878-880. Breig, A. (1960) Biomechanics ofrhe Cenrral Nervous System Almquist & Wiksell, Stockholm. Dohrmann, G. J. and Panjab, M. M. (1976) Standardized spinal cord trauma: biomechanical parameters and lesion volume. Surg. Neural. 6, 263-267. Hung, T. K., Albin, M. S., Brown, T. D., Bunegin, L., Albin, R. and Jannetta, P. J. (1975) Biomechanical responses to open experimental spinal cord injury. Surg. Neural. 4, 271-276. Hung,T. K., Lin, H. S.,Albin, M. S., Bunegin, L. and Jannetta, P. J. (1979a) The standardization of experimental impact injury to the spinal cord. Surg. Neural. 11, 470-477. Hung, T. K., Chang, G. L., Lin, H. S., Chang, J. L. and Feng, W. W. (1979b). Biorheology and experimental trauma of spinal cord of cats. Proc. Third ASCE Engng Mech. DII Speciality Coflj Hung, T. K. and Chang, G. L. (1981). Biomechanical and neurological responses of the spinal cord of puppy to uniaxial tensions. J. biomed. Engng. ASMG (in press). White, R. J. and Albin, M. S. (1970) Spine and spinal cord injury. In Impact Injury and Crash Protection (Edited by Gurdjian, E. S., Lange, W. A., Patrick, L. M. and Thomas L. M. pp. 63-84. Charles C. Thomas, Springfield, Illinois.
Department
of Neurological
Surgery and Department of Civil Engineering, University of Pittsburgh. Pittsburgh. PA 15261, U .S.A
TIN-KAN HL~(; GUAN-LIANG CHAN(, HSIN-SL.N LI\ FRAW R. WAI.TLR LEON BLX=+~;I\