Journal of the neurological Sciences, 1975, 24:299-304
299
t~ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
A Pressure Vessel Model for Nerve Compression R. J. MACGREGOR*, S. K. SHARPLESS ANDM. W. LUTTGES Departments of Engineering Design and Economic Evaluation ( R.J.M. ) , Psychology ( S.K.S. ) and Aerospace and Engineering Sciences (M. W.L.), University of Colorado, Boulder, Colo. 80302 (U.S.A.) (Received 25 July, 1974)
INTRODUCTION
A block of conduction in nerve by localized pressure is not an uncommon clinical entity. Compression block is believed to be responsible for a number of disorders associated with trauma to the spine, herniated discs, carpal tunnel syndrome, "Saturday night" syndrome, and others. It has been the subject of an extensive clinical and experimental literature (Sunderland 1968). It has been known for over a century that the various modalities of sensation are differentially affected when pressure is applied to a sensory nerve. Thus, contact sensation is obtunded before pain and temperature sensation are lost. This received an explanation in the observation that large-diameter fibers, carrying contact sensations, are more susceptible to compression than small-diameter fibers, carrying pain and thermal sensation (Gasser and Erlander 1929). Recently, the relative susceptibility of large fibers to compression block has acquired additional significance owing to the I~lelzack-Wall theory of pain (Melzack and Wall 1965). According to this theory, activity in large sensory nerve fibers tends to suppress pain signals upon their entrance to the spinal cord by presynaptic inhibition, and, therefore, selective block of large fibers by moderate compression should exacerbate pain sensations arising in the affected segment. Despite numerous investigations of compression block, there is still, to our knowledge, no satisfactory explanation of the relation of fiber diameter to susceptibility to compression block. Indeed, the mechanism of compression block is not fully understood, the roles of ischemia and constriction not having been entirely disentangled (Bentley and Schlapp 1943; Causey and Palmer 1949; Gelfan and Tarlov 1956; Tarlov 1957). The purpose of this note is to show that with certain assumptions, classic mechanical principles imply that large fibers undergo more constriction than small fibers when subjected to the same compressive pressure. Thus, if conduction
* Dr. MacGregor's contribution to this work has been supported by National Science Foundation Grant Number GB-33687 and by Grant Number I R01/NS10781-01 of the National Institute of Neurological Diseases and Stroke. Dr. Sharpless' and Dr. Luttges' contributions have been supported by the International Chiropractor's Association and the American Chiropractic Association.
300
R. J, M A C G R E G O R , S. K. S H A R P L E S S , M. W . L U I I'G[!S
block depends on the proportional decrease in cross-sectional area of a nerve fiber. the greater susceptibility of large fibers to compression block can be accounted for on simple mechanical principles. Several investigators have attempted to study the phenomena of nerve compression on the basis of more-or-less rigid tube models wherein the anatomical nerve is assumed to consist of a bundle of plastic or rubber tubes, each of which represents a single nerve fiber. Weiss and Hiscoe (1948) for example performed several experiments on such a model system. They showed that a bundle of hollow rubber tubes when squeezed exhibited differentially more compression in peripheral areas than in the center of the bundle. Studies in our own laboratories on plastic tube models have confirmed and extended Weiss and Hiscoe's observations. These model studies show larger percentage deformation in large-diameter tubes than in small-diameter tubes, as well as the differential deformation in peripheral tubes found by Weiss and Hiscoe (Luttges 1973). However, we have come to the opinion that such rigid tubes are not a very good representation of the reaction of nerves to compression : the resistance to compression in such models derives largely from their wall properties, whereas this would not seem to be the case for real nerve fibers whose membranes are exceedingly thin and malleable. We have, therefore, developed an alternative model for nerve compression wherein basic concepts from pressure vessel theory are applied to a "sausage" model for nerve fibers. THE MODEL
For purposes of resistance to localized compression we suppose that a nerve fiber can be reasonably modeled by an incompressible fluid surrounded by a thin elastic membrane in the shape of a circular cylinder. We suppose that the membrane is highly non-rigid and might collapse if not filled with fluid. When such a model nerve is squeezed over a localized interval the fluid under the compressed area is displaced and must distend the membrane at other places in the element. The main factor in its resistance to compression is the elasticity of the membrane at locations where the displaced fluid provides forces to distend it. In order to gain a qualitative assessment of the behavior exhibited by such a model nerve it is convenient to make several highly simplifying assumptions. Assume the nerve compresses under the applied pressure~ P, until the internal pressure is equal to the applied pressure. Assume also that the internal pressure is uniform throughout the element and is then balanced by hoop stresses in the surrounding membrane. This situation is indicated in Fig. 1. Suppose also that similar elastic effects at the closed ends of the nerve cell are effected by longitudinal stresses which can be represented by a spring at the " e n d " of the cylinder. The essential mechanism of deformation in the sausage pressure vessel model for nerve compression is the following: to attain the internal pressure needed to balance an external pressure P applied at a locus of compression, the surrounding membrane in adjacent regions must provide a hoop stress to balance the pressure, P, exerted by displaced fluid. To develop such hoop stresses the membrane must first stretch according to its elastic properties. Since large fibers require larger hoop stresses to match a given internal pressure, they will correspondingly exhibit a larger percentage membrane stretch assuming
301
A PRESSURE VESSEL MODEL FOR NERVE COMPRESSION
/ / ~ deformedshape
~az
S initialshape LJ_LLL_
r? II
l
I
I"
"1
P
#w
,r~X
,,ix
• Fig. 1. Pressure vessel model for nerve compression.
only that the stress-strain relationship for the membrane is monotonic. By making further assumptions one can obtain quantitative estimates of the deformation and relative compressibility exhibited by such model nerves, which can illustrate more precisely the basic mechanisms suggested here and moreover provide the groundwork for subsequent analytic refinement of the theory. This highly simplified model predicts that the percentage deformation in individual model nerve fibers is approximately proportional to fiber diameter. Assume that the applied external pressure, P, causes radial compression 61 over a length A, and consequent displacement of fluid volume equal 27rA61 as indicated in Fig. 1. Assume that this displaced fluid forces radial distension 62of the membrane at adjacent areas along the length 1, and longitudinal displacement, 6a, at the "end" of the cylinder. Spring constants Kcq, K', and K, are defined by equations (1):
P=K' (~)
(1)
Note that these constants determine percentage deformation in terms of pressure. Another basic equation is obtained by demanding conservation of mass for the incompressible fluid as in equation (2): zrr2 63 + 2nr162 =
2ztrA61
(2)
From these expressions we obtain the expression for the displacement under the applied pressure, 61, in terms of 02 and 63 as given in equation (3), and the expression
302
R. J. MACGREGOR, S. K. SHARPLESS, M. W. LU'FTGES
for the equivalent spring constant for compression, Keq, in terms of the membrane spring constants K' and K, also given in equation 3" l
1
1
Note that the spring constant Keq measures the relative compressibility of the fiber directly under the applied pressure. We can now determine K' and K in terms of the properties of the membrane under the displacements 62 and 63. For example, if we assume a linear stress-strain relationship for the membrane and apply simplified pressure vessel theory to the cylindrical region we can write equation (4):
ah ~h-
Pr
E '
(71
[A(~h
Pr
E '
az = 2 t
e~- E
eh =
I~
E
6h-~--t"
2rt(r + 62) - 2r~r 2r~r
(4)
az r
63 Here, ah and ~ are the hoop stress and longitudinal stress in the membrane, respectively. The corresponding hoop and longitudinal strains are eh and e~. E and ~ are elastic constants of the membrane. The expressions relating the stresses, trh and e~, to the internal pressure, P, are classical results in pressure vessel theory. They represent the balance of forces required to keep the membrane stationary. These relationships are the basis of the eventual deduction that the percentage deformation will be larger in larger diameter fibers. From equations (4) one can determine the percentage deformations 62/r and 6all in terms of P, and thereby obtain the spring constants K' and K as given in equations (5):
tE /6~\ P - r(1-/z/2) ~-~) , P-
tE (~) r(1/2-/~)
K'-
, K
tE r(1-#/2) tE r(1/2-/~)
(5)
The essential point is that the spring constants K' and K depend inversely on the cylinder radius, r. Finally, then, the equivalent spring constant, Keq, which measures the relative compressibility of the sausage model is given in terms of cylinder geometry and mem-
A PRESSURE VESSEL MODEL FOR NERVE COMPRESSION
303
brane properties in equation (6): tE
(6)
Keq= r ( l ) [5/4_l~ ] c~1 for a given From equations (1) and (6) one sees that the percentage compression,--, r applied pressure, P, is directly proportional to the radius of the cylinder, r. Moreover, the percentage lateral and longitudinal extensions, 62/r and c~3/l , are also proportional to r, as may be seen from equations (5). •
DISCUSSION
These equations, although highly instructive should be taken primarily as qualitative guidelines• For example, if the membrane exhibits a non-linear stress-strain relationship wherein the strain is progressively more pronounced as the stress increases which is quite typical of biological materials, then the predicted higher level of stress for larger fibers in this pressure vessel model could conceivably result in a considerably higher deformation. Moreover, if the difference in stress between the larger and smaller diameter cases were such that the stress in the larger diameter was greater than some critical level whereas that in the smaller diameter fiber was not, rupture might very well occur in the larger fiber with much less severe effects noticeable in the smaller fibers. The highly simplified analytical approach developed here to obtain the main qualitative picture should be refined in future work. Thus, one would like to consider longitudinal variations of pressure and deformation in the model, non-linear viscoelastic membrane properties, and a more realistic representation of end effects. This is a tractable problem which can be precisely formulated in engineering terms, but which will require numerical techniques for solution. Recently Ochoa, Fowler and Gilliatt (1972) found a characteristic anatomical change associated with chronic applied pressure. This lesion consisted of lateral movement of the nodes of Ranvier proximal and distal to the compressive cuff. The change was brought about by an extension of myelin on the side of the node nearest to the cuff and subsequently an invagination of myelin on the side of the node furthest away from the cuff. They argue that this change is the result of direct pressure and not a secondary result of ischemia and suggest that the primary event is the displacement of axoplasm from under the cuffdue to an internal pressure gradient. They further suggest that the axoplasm might meet resistance to longitudinal motion at nodes of Ranvier which could be due to a narrowing of the axon tube at such nodes. If this narrowing is less prominent in small fibers it could then account for the preferential occurrence of the lesion in large myelinated fibers. Our model predicts the existence of hoop and longitudinal stresses in neural membrane, and we could further suggest that the unsupported membrane between myelin sheaths at nodes of Ranvier could be most susceptible to damage from internal pressure. However, more extensive analytical elaboration would be required to predict the reaction of this compound system. Also, we should note that their lesion is pro-
304
R. J. MACGREGOR, S. K. SHARPLESS, M. W. LUTTGES
duced in a chronic preparation wherein the cuff is applied for several hours and the nerve examined weeks later. It seems quite likely that this lesion might involve longterm plastic effects of some portion of the neuronal apparatus as a natural consequencc of its being subjected to sustained internal pressure over several hours. If the neuronal membrane participates in such a process the preferential sensitivity of large fibers to the lesion in their data could reflect the larger hoop and longitudinal stresses predicted for larger fibers by our pressure vessel model. On the other hand, active degenerating and regenerating processes undoubtedly occur in this chronic preparation. Such processes quite possibly contribute to the form of the observed lesion.
SUMMARY
This paper suggests that compression block in nerve can be better interpreted in terms of a pressure vessel model for nerve fiber distension that the more common models based upon tubes with more or less rigid walls. In this model resistance to compression is due to the elasticity of the cell membrane at locations where displaced intracellular fluid tends to distend it. Because the stresses in pressure vessels increase with the size of the vessel, the theory predicts that the percentage deformation should be larger in larger diameter fibers. REFERENCES BENTLEY, F. H. AND W. SCHLAPP (1943) The effects of pressure on conduction in peripheral nerve, d. Physiol. (Lond.), 102: 72-82. CAUSEY, G. AND E. PALMER(1949) The effect of pressure on nerve conduction and nerve-fibre size, J. Physiol. (Lond.), 109: 220-231. GASSER,H. S. ANDJ. ERLANDER(1929) The role of fiber size in the establishment of a nerve block by pressure or cocaine, Amer. J. Physiol., 88: 581-591. GE£FAN, S. AND I. M. TARLOV(1956) Physiology of spinal cord, nerve root and peripheral nerve compression, Amer. J. Physiol., 185: 217-229. LUTTGESp M. W. (1973) Studies of parameters relating to spinal dysfunctions. In: C. H. SUH (Ed.), Biomechanics Confe~nce on the Spine, University of Colorado, pp. 1-55. MELZACK, R. AND P. D. WALL (1965) Pain mechanism: A new theory, Science, 150: 971-979. OCEIOA,J., T. J. FOWLERAND R. W. GILLIATT (1972) Anatomical changes in peripheral nerves compressed by a pneumatic tourniquet, J. Anat. (Lond.), 113: 433-455. SUNDERLAND, S. (1968) Nerves and Nerve Injury, Churchill Livingstone, Edinburgh. TARLOV,I. M. (1957) Spinal Cord Compression: Mechanism of Paralysis and Treatment, Thomas, Springfield, Ill. WEISS, P. AND H. H. HISCOE (1948) Experiment on the mechanism of nerve growth, J. exp. Zool., 107: 315-393.
299
t~ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
A Pressure Vessel Model for Nerve Compression R. J. MACGREGOR*, S. K. SHARPLESS ANDM. W. LUTTGES Departments of Engineering Design and Economic Evaluation ( R.J.M. ) , Psychology ( S.K.S. ) and Aerospace and Engineering Sciences (M. W.L.), University of Colorado, Boulder, Colo. 80302 (U.S.A.) (Received 25 July, 1974)
INTRODUCTION
A block of conduction in nerve by localized pressure is not an uncommon clinical entity. Compression block is believed to be responsible for a number of disorders associated with trauma to the spine, herniated discs, carpal tunnel syndrome, "Saturday night" syndrome, and others. It has been the subject of an extensive clinical and experimental literature (Sunderland 1968). It has been known for over a century that the various modalities of sensation are differentially affected when pressure is applied to a sensory nerve. Thus, contact sensation is obtunded before pain and temperature sensation are lost. This received an explanation in the observation that large-diameter fibers, carrying contact sensations, are more susceptible to compression than small-diameter fibers, carrying pain and thermal sensation (Gasser and Erlander 1929). Recently, the relative susceptibility of large fibers to compression block has acquired additional significance owing to the I~lelzack-Wall theory of pain (Melzack and Wall 1965). According to this theory, activity in large sensory nerve fibers tends to suppress pain signals upon their entrance to the spinal cord by presynaptic inhibition, and, therefore, selective block of large fibers by moderate compression should exacerbate pain sensations arising in the affected segment. Despite numerous investigations of compression block, there is still, to our knowledge, no satisfactory explanation of the relation of fiber diameter to susceptibility to compression block. Indeed, the mechanism of compression block is not fully understood, the roles of ischemia and constriction not having been entirely disentangled (Bentley and Schlapp 1943; Causey and Palmer 1949; Gelfan and Tarlov 1956; Tarlov 1957). The purpose of this note is to show that with certain assumptions, classic mechanical principles imply that large fibers undergo more constriction than small fibers when subjected to the same compressive pressure. Thus, if conduction
* Dr. MacGregor's contribution to this work has been supported by National Science Foundation Grant Number GB-33687 and by Grant Number I R01/NS10781-01 of the National Institute of Neurological Diseases and Stroke. Dr. Sharpless' and Dr. Luttges' contributions have been supported by the International Chiropractor's Association and the American Chiropractic Association.
300
R. J, M A C G R E G O R , S. K. S H A R P L E S S , M. W . L U I I'G[!S
block depends on the proportional decrease in cross-sectional area of a nerve fiber. the greater susceptibility of large fibers to compression block can be accounted for on simple mechanical principles. Several investigators have attempted to study the phenomena of nerve compression on the basis of more-or-less rigid tube models wherein the anatomical nerve is assumed to consist of a bundle of plastic or rubber tubes, each of which represents a single nerve fiber. Weiss and Hiscoe (1948) for example performed several experiments on such a model system. They showed that a bundle of hollow rubber tubes when squeezed exhibited differentially more compression in peripheral areas than in the center of the bundle. Studies in our own laboratories on plastic tube models have confirmed and extended Weiss and Hiscoe's observations. These model studies show larger percentage deformation in large-diameter tubes than in small-diameter tubes, as well as the differential deformation in peripheral tubes found by Weiss and Hiscoe (Luttges 1973). However, we have come to the opinion that such rigid tubes are not a very good representation of the reaction of nerves to compression : the resistance to compression in such models derives largely from their wall properties, whereas this would not seem to be the case for real nerve fibers whose membranes are exceedingly thin and malleable. We have, therefore, developed an alternative model for nerve compression wherein basic concepts from pressure vessel theory are applied to a "sausage" model for nerve fibers. THE MODEL
For purposes of resistance to localized compression we suppose that a nerve fiber can be reasonably modeled by an incompressible fluid surrounded by a thin elastic membrane in the shape of a circular cylinder. We suppose that the membrane is highly non-rigid and might collapse if not filled with fluid. When such a model nerve is squeezed over a localized interval the fluid under the compressed area is displaced and must distend the membrane at other places in the element. The main factor in its resistance to compression is the elasticity of the membrane at locations where the displaced fluid provides forces to distend it. In order to gain a qualitative assessment of the behavior exhibited by such a model nerve it is convenient to make several highly simplifying assumptions. Assume the nerve compresses under the applied pressure~ P, until the internal pressure is equal to the applied pressure. Assume also that the internal pressure is uniform throughout the element and is then balanced by hoop stresses in the surrounding membrane. This situation is indicated in Fig. 1. Suppose also that similar elastic effects at the closed ends of the nerve cell are effected by longitudinal stresses which can be represented by a spring at the " e n d " of the cylinder. The essential mechanism of deformation in the sausage pressure vessel model for nerve compression is the following: to attain the internal pressure needed to balance an external pressure P applied at a locus of compression, the surrounding membrane in adjacent regions must provide a hoop stress to balance the pressure, P, exerted by displaced fluid. To develop such hoop stresses the membrane must first stretch according to its elastic properties. Since large fibers require larger hoop stresses to match a given internal pressure, they will correspondingly exhibit a larger percentage membrane stretch assuming
301
A PRESSURE VESSEL MODEL FOR NERVE COMPRESSION
/ / ~ deformedshape
~az
S initialshape LJ_LLL_
r? II
l
I
I"
"1
P
#w
,r~X
,,ix
• Fig. 1. Pressure vessel model for nerve compression.
only that the stress-strain relationship for the membrane is monotonic. By making further assumptions one can obtain quantitative estimates of the deformation and relative compressibility exhibited by such model nerves, which can illustrate more precisely the basic mechanisms suggested here and moreover provide the groundwork for subsequent analytic refinement of the theory. This highly simplified model predicts that the percentage deformation in individual model nerve fibers is approximately proportional to fiber diameter. Assume that the applied external pressure, P, causes radial compression 61 over a length A, and consequent displacement of fluid volume equal 27rA61 as indicated in Fig. 1. Assume that this displaced fluid forces radial distension 62of the membrane at adjacent areas along the length 1, and longitudinal displacement, 6a, at the "end" of the cylinder. Spring constants Kcq, K', and K, are defined by equations (1):
P=K' (~)
(1)
Note that these constants determine percentage deformation in terms of pressure. Another basic equation is obtained by demanding conservation of mass for the incompressible fluid as in equation (2): zrr2 63 + 2nr162 =
2ztrA61
(2)
From these expressions we obtain the expression for the displacement under the applied pressure, 61, in terms of 02 and 63 as given in equation (3), and the expression
302
R. J. MACGREGOR, S. K. SHARPLESS, M. W. LU'FTGES
for the equivalent spring constant for compression, Keq, in terms of the membrane spring constants K' and K, also given in equation 3" l
1
1
Note that the spring constant Keq measures the relative compressibility of the fiber directly under the applied pressure. We can now determine K' and K in terms of the properties of the membrane under the displacements 62 and 63. For example, if we assume a linear stress-strain relationship for the membrane and apply simplified pressure vessel theory to the cylindrical region we can write equation (4):
ah ~h-
Pr
E '
(71
[A(~h
Pr
E '
az = 2 t
e~- E
eh =
I~
E
6h-~--t"
2rt(r + 62) - 2r~r 2r~r
(4)
az r
63 Here, ah and ~ are the hoop stress and longitudinal stress in the membrane, respectively. The corresponding hoop and longitudinal strains are eh and e~. E and ~ are elastic constants of the membrane. The expressions relating the stresses, trh and e~, to the internal pressure, P, are classical results in pressure vessel theory. They represent the balance of forces required to keep the membrane stationary. These relationships are the basis of the eventual deduction that the percentage deformation will be larger in larger diameter fibers. From equations (4) one can determine the percentage deformations 62/r and 6all in terms of P, and thereby obtain the spring constants K' and K as given in equations (5):
tE /6~\ P - r(1-/z/2) ~-~) , P-
tE (~) r(1/2-/~)
K'-
, K
tE r(1-#/2) tE r(1/2-/~)
(5)
The essential point is that the spring constants K' and K depend inversely on the cylinder radius, r. Finally, then, the equivalent spring constant, Keq, which measures the relative compressibility of the sausage model is given in terms of cylinder geometry and mem-
A PRESSURE VESSEL MODEL FOR NERVE COMPRESSION
303
brane properties in equation (6): tE
(6)
Keq= r ( l ) [5/4_l~ ] c~1 for a given From equations (1) and (6) one sees that the percentage compression,--, r applied pressure, P, is directly proportional to the radius of the cylinder, r. Moreover, the percentage lateral and longitudinal extensions, 62/r and c~3/l , are also proportional to r, as may be seen from equations (5). •
DISCUSSION
These equations, although highly instructive should be taken primarily as qualitative guidelines• For example, if the membrane exhibits a non-linear stress-strain relationship wherein the strain is progressively more pronounced as the stress increases which is quite typical of biological materials, then the predicted higher level of stress for larger fibers in this pressure vessel model could conceivably result in a considerably higher deformation. Moreover, if the difference in stress between the larger and smaller diameter cases were such that the stress in the larger diameter was greater than some critical level whereas that in the smaller diameter fiber was not, rupture might very well occur in the larger fiber with much less severe effects noticeable in the smaller fibers. The highly simplified analytical approach developed here to obtain the main qualitative picture should be refined in future work. Thus, one would like to consider longitudinal variations of pressure and deformation in the model, non-linear viscoelastic membrane properties, and a more realistic representation of end effects. This is a tractable problem which can be precisely formulated in engineering terms, but which will require numerical techniques for solution. Recently Ochoa, Fowler and Gilliatt (1972) found a characteristic anatomical change associated with chronic applied pressure. This lesion consisted of lateral movement of the nodes of Ranvier proximal and distal to the compressive cuff. The change was brought about by an extension of myelin on the side of the node nearest to the cuff and subsequently an invagination of myelin on the side of the node furthest away from the cuff. They argue that this change is the result of direct pressure and not a secondary result of ischemia and suggest that the primary event is the displacement of axoplasm from under the cuffdue to an internal pressure gradient. They further suggest that the axoplasm might meet resistance to longitudinal motion at nodes of Ranvier which could be due to a narrowing of the axon tube at such nodes. If this narrowing is less prominent in small fibers it could then account for the preferential occurrence of the lesion in large myelinated fibers. Our model predicts the existence of hoop and longitudinal stresses in neural membrane, and we could further suggest that the unsupported membrane between myelin sheaths at nodes of Ranvier could be most susceptible to damage from internal pressure. However, more extensive analytical elaboration would be required to predict the reaction of this compound system. Also, we should note that their lesion is pro-
304
R. J. MACGREGOR, S. K. SHARPLESS, M. W. LUTTGES
duced in a chronic preparation wherein the cuff is applied for several hours and the nerve examined weeks later. It seems quite likely that this lesion might involve longterm plastic effects of some portion of the neuronal apparatus as a natural consequencc of its being subjected to sustained internal pressure over several hours. If the neuronal membrane participates in such a process the preferential sensitivity of large fibers to the lesion in their data could reflect the larger hoop and longitudinal stresses predicted for larger fibers by our pressure vessel model. On the other hand, active degenerating and regenerating processes undoubtedly occur in this chronic preparation. Such processes quite possibly contribute to the form of the observed lesion.
SUMMARY
This paper suggests that compression block in nerve can be better interpreted in terms of a pressure vessel model for nerve fiber distension that the more common models based upon tubes with more or less rigid walls. In this model resistance to compression is due to the elasticity of the cell membrane at locations where displaced intracellular fluid tends to distend it. Because the stresses in pressure vessels increase with the size of the vessel, the theory predicts that the percentage deformation should be larger in larger diameter fibers. REFERENCES BENTLEY, F. H. AND W. SCHLAPP (1943) The effects of pressure on conduction in peripheral nerve, d. Physiol. (Lond.), 102: 72-82. CAUSEY, G. AND E. PALMER(1949) The effect of pressure on nerve conduction and nerve-fibre size, J. Physiol. (Lond.), 109: 220-231. GASSER,H. S. ANDJ. ERLANDER(1929) The role of fiber size in the establishment of a nerve block by pressure or cocaine, Amer. J. Physiol., 88: 581-591. GE£FAN, S. AND I. M. TARLOV(1956) Physiology of spinal cord, nerve root and peripheral nerve compression, Amer. J. Physiol., 185: 217-229. LUTTGESp M. W. (1973) Studies of parameters relating to spinal dysfunctions. In: C. H. SUH (Ed.), Biomechanics Confe~nce on the Spine, University of Colorado, pp. 1-55. MELZACK, R. AND P. D. WALL (1965) Pain mechanism: A new theory, Science, 150: 971-979. OCEIOA,J., T. J. FOWLERAND R. W. GILLIATT (1972) Anatomical changes in peripheral nerves compressed by a pneumatic tourniquet, J. Anat. (Lond.), 113: 433-455. SUNDERLAND, S. (1968) Nerves and Nerve Injury, Churchill Livingstone, Edinburgh. TARLOV,I. M. (1957) Spinal Cord Compression: Mechanism of Paralysis and Treatment, Thomas, Springfield, Ill. WEISS, P. AND H. H. HISCOE (1948) Experiment on the mechanism of nerve growth, J. exp. Zool., 107: 315-393.
