AMERICAN JOURNAL Vol. 230, No. 4, April
Elastic
OF
PHYSIOL~CY 1976. Prtnted
UI U.S.A.
behavior
of brain
tissue
in vivo
E. K. WALSH AND A. SCHETTINI University of Florida, Gainesville, Florida 32611; and Veterans Hospital Center, Los Angeles, California 90073
brain elastic response; pressure
brain
METHODS
tis-
AND IDENTIFICATION ofthe response behavior of the intracranial system is important for purposes of relating changes in the condition of the system, in particular the brain, to controlled variations, e.g., intracranial hypertension, inhalation of anesthetic agents, hyperventilation, etc. It is well known that brain tissue exhibits viscoelastic behavior (1, 3, 7); thus the mechanical response properties that identify the behavior include pressure relaxation, creep displacement, and the short-time or elastic response. This last property is particularly useful in a quantitative evaluation of that property usually described by the terms “soft” or “tight .” Here we describe a system for the measurement and evaluation of the elastic response of brain tissue in vivo through the intact dura. The experimental tests yield simultaneous pressure and displacement (insertion depth) measurements from which the elastic response or its inverse, the compliance, can be determined. The evaluation of the in vivo response properties of brain tissue, however, does require the certainty that the pressure-depth measurements are made in the subpial region. This determination is part of the experimental program involved in the elastic-response measurements and is described in RESULTS. The method differs significantly from that described previously by Schettini and Walsh (8). Finally, since the direct experi-
THE MEASUREMENT
Wadsworth
mental measurements represent an indication of the elastic behavior, rather than the classical elastic response modulus, we discuss a means of deriving the elastic modulus from the pressure-displacement measurements and compare these results with those reported elsewhere.
WALSH, E. K., AND A. SCHETTINI. EZastic behavior of brain tissue in vivo. Am. J. Physiol. 230(4): 1058-1062. 1976. -A measurement system and a test sequence have been developed to determine the in vivo elastic response of brain tissue in terms of a pressure-depth ratio. This parameter appears sensitive to changes in the tissue environment that may occur due to the influence of, e.g., anesthetic agents, hyperventilation, etc., and thus may be useful in evaluating such influences. The measurements are made with the dura-arachnoid membranes intact, thus maintaining the influence of the cerebrospinal fluid compartment on the response behavior of the brain tissue that comprises the subpial region. As an integral part of the test, the procedure also serves to determine the depth or position of the subpial region and thus assures that the subsequent pressure-depth measurements involve brain tissue response. Finally, some discussion is given to relating the measured pressure-depth ratio to the classical elastic modulus. Values of the pressure-depth ratio and the corresponding elastic modulus for seven dogs are given. bra in mechanical properties; sue compliance; intracranial
Administration
AND
PROCEDURE
Transducer and instrumentation. The transducer, shown schematically in Fig. 1, has been described at length elsewhere (9). Basically it involves a movableshaft system contained within a barrel that is firmly attached to a stainless steel collar implanted on the animal skull. The dura-arachnoid membranes are left intact; thus the influence of the cerebrospinal fluid on the measured system response is retained. A pressuresensitive element (type P-18 implantable transducer, Konigsberg Instruments, Inc., Pasadena, Calif.) is mounted in the base of the piston and secured by a rigid coplanar ring that serves to remove any measure of the tensile forces associated with the dura-arachnoid membranes. The displacement is measured by a linear variable-differential transformer (type 250-MHR LVDT, Schaevitz Engineering, Pennsauken, N. J.) whose core is mounted colinearly with the piston. Thus, the configuration of the instrument allows a rapid insertion of the pressure transducer into the intracranial cavity with a simultaneous recording of the pressure and the depth of insertion. The core-shaft collar can be preset to allow an initial displacement; then, advancing or withdrawing the depth-control cylinder provides controlled incremental changes in the insertion depth. Animal preparation. The measurements described here were made on dogs (15-25 kg) with the transducer mounted on a collar that had been implanted on a small burr hole (1.6 cm OD). The collar implantation was carried out with sterile techniques and general anesthesia, as described previously (7). Test procedure. Approximately 45 min before a test the animal was sedated lightly Innovar-Vet, 0.1 mg/kg iv). Additional sedation during the tests was provided by intermittent doses of thiopental (25-50 mg) given intravenously. Shortly before the test, the dog was placed in a reclining position and the transducer mounted to the implanted collar. The measurements were then made as follows: with the core-shaft collar fixed, the threaded depth-control cylinder, which serves to limit the depth of travel of the piston, was inserted into the transducer housing to a predetermined depth.
1058 Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
ELASTIC
RESPONSE
OF
BRAIN
Y-
TISSUE
IN
1059
VIVO
corresponding insertion depth, 8,, associated with the brain surface, i.e., the subpial region, prior to compression of the tissue within that region. In Fig. 2 the values of ps and 6, for dog 819 determined just prior to the elastic-response test are shown. In Fig. 3 the results of the elastic-response test shown
LVDT
core shaft
collar
depth control cylinder
barrel piston implan t collar A FIG.
1. Pressure-displacement
pressure transducer transducer.
Then the piston, and consequently the pressure-sensing transducer, was rapidly inserted (manually), causing a rise in pressure. The resulting pressure and depth were recorded on a graphic recorder. The piston was held at this insertion depth for approximately 2 s, then withdrawn, after which the system was allowed to recover for lo-15 min. Next the depth-control cylinder was repositioned a predetermined amount within the barrel, which resulted in a slightly greater insertion depth for the subsequent measurement. A sequence of such insertions, separated by periods of recovery, made up the elastic-response (compliance) test. Figure 2 shows the results of one such test (dog 619). The upper trace represents the transducer displacement and the lower trace the pressure response. The peak pressure versus the corresponding peak displacement yields the elastic response. These results for seven animals are discussed in the following section.
I 4
-- - ps ___- - - - __- _j - - - - - - - . I I L .
L v
Time FIG.
depth depth
.
.
i
.
L
.
L .
.
1
b 10 set
2. Elastic-response test for dog 819. Upper and lower trace is corresponding pressure; and pressure of subpial region.
trace is insertion 6, and pd identify
RESULTS
Elastic response (compliance). These tests were designed to determine the in vivo dynamic response of brain tissue, i.e., of the material in the subpial region of the intracranial system under the influence of a closed cerebrospinal fluid (CSF) compartment. It follows then that it was necessary to assure that the measurements attributed to the subpial material were indeed made in that region; i.e., the positions of the subregions of the system must be determined. This was done through a procedure developed by the present authors (8) and confirmed by an alternative method recently devised that is described in the next subsection. The results of these procedures yield the pressure, designated as pg. and
I
3 FIG.
values shown
3. Elastic-response of peak pressure in Fig. 2.
1
1
1
4
I
5
lnserrlon Depth - mm test results for dog 819. Circles and peak insertion depth for
Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
I
represent insertions
1060
E. K.
in Fig. 2 are presented with the values of the individual insertions indicated as the experimental points. In exhibiting these results we have taken pressure as the vertical scale and insertion depth as the horizontal. Thus the slope (or range of slope) Ap/A6 represents an elastic response or a (pseudo)elastic modulus.’ The inverse AS/Ap is an indication of the short-time or dynamic compliance and the value a (pseudo)compliance modulus. The break in the “curve” between the two ranges of nearly constant slope -identified as pS, 8, -is significant and is discussed in the next subsection. Of course the elastic response of the brain tissue is associated with the slope beyond the position 6,. However, since this position varies among animals, a more meaningful comparison of the elastic response of several animals is obtained if the graph of each is shifted so as to originate at the pointp,, & (thus, in essence, graphically subtractingp,, 6, from the values of pressure and depth for each insertion). This has been done for dog 619 in Fig. 4 along with the results of other tests, again with pressure as the vertical scale.’ To give a quantitative measure to the results we evaluate the slopes directly in terms of the parameter G,, = AplA6 in the units measured (mmHg/mm). The results for the tests shown in Fig. 4 are given in Table 1. In these tests great care was taken to maintain normal physiological conditions. Thus, from these results we consider the range of G, from approximately 15 to 25 mmHg/mm as the pressuredepth ratio for brain tissue under normal conditions. These values of pressure-depth ratio are useful directly in this form as a measure of the tissue response under normal conditions for comparison with similar values measured under controlled changes. However, in order to relate the results to measurements made with other configurations it is necessary to use the measured pressures and depths in the solution of the mechanics problem that approximates the experimental configuration. This is taken up in a later subsection. Determination Determination ofposition ofposition of subpial region from elastic-response test. In reference 8 a method was reported that used the results of tests with a controlled insertionrate pressure transducer to determine the position of the subpial region of the intracranial system that we identify as the brain surface. In that study a motor-controlled pressure transducer was used in tests that involved a uniform insertion of the pressure-sensing element at a constant rate to a depth corresponding to a predetermined pressure, followed by a uniform withdrawal. A detectable change in the pressure response was taken as an indication of a change in the material, i.e., a change in the system representing distinct regions of the intracranial system. Figure 5 shows the results of a test of constant insertion pressure on dog 819. The change in slope of the pressure response at an insertion depth of approximately 4.2 mm is taken to be I The reason for the appellation “pseudo” is discussed later in this section. z The single line in Fig. 4 for dog 819 represents an approximate best-fit to the experimental points (cf. Fig. 3), as was done for the other tests.
?
I
I
1
1 .5
WALSH
I
AND
A. SCHETTINI
I
I
I I.0
1
*
1
a IO
01 0
1
b-b, 4. Results represent best-fit FIG.
I 1.5
1
-mm
of elastic-response tests in 7 dogs. Sloping approximations to experimental points.
lines
1. Mechanical para meters of brain tissue elastic response in 7 dogs
TABLE
G,, mmHg/mm
DOC: 819 770 854 811 828 784 885 Mean + SD * Based
on model
E *, x 10’ dynes/cm’
2.80 3.01 3.01 3.10 3.30 4.01 4.12 3.3 ?I 0.52
17.3 18.6 18.6 19.2 20.4 24.8 25.5 20.6 + 3.2 and assumptions
discussed
in
RESULTS.
the position of the brain surface3 at the time of this particular test. As one might expect, this determination can also be made from the results of the elastic-response test. That is, since the hypothesis is that the incremental change in pressure associated with an incremental change in insertion depth is a measure of the elastic response of the material in the region where the measurements are made, then it would be expected that this ratio would change as the pressure transducer moved from one region to the other. Thus, in the present configuration, if the initial insertions are carried out within the CSF-transition regions and subsequent insertions within the subpial region, we would expect to see a difference in the pressure-depth ratios associated with each. Figure 3 shows such a change in slope with the point of change labeled as pwq,6,. -Here &is approximately 4. 0 mm. A.lthough this corn.pares to the value obtained from the pressure test to within the experi3 We define the position which subsequent insertion of the subpial region.
of the brain surface as that depth beyond involves compression of the brain tissue
Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
ELASTIC
RESPONSE
OF
BRAIN
TISSUE
IN
1061
VIVO 6
5
I” E z” E
ratio. The value assumed for 7 was 0.5 (5). With G, in units of millimeters of Hg per millimeter and the radii in units of millimeters, E is in units of millimeters of Hg. Converting this to dynes per square centimeter, the range of values of G, in Table 1 corresponds to moduli of 2.8-4.1 x 10” dynes/cm? This compares with a value of 2 x 10:) dynes/cm2 reported by Metz, McElhaney, and Ommaya (5) for the lowest values of strain in their tests. DISCUSSION
0
Time FIG.
onset
5. Pressure test for dog of subpial region (see text).
-
min
819.
Region
marked
6, indicates
mental accuracy of +O. 1 mm insertion depth, there may also have occurred a slight shift in position during the time between the pressure test and the elastic-response test. from pressureDetermination of elastic modulus The results of th .e pressure-depth depth measurements,
measurements yield a slope or pressure-depth ratio that not only reflects the elastic response of the subpial terial but also the test confi .guration and geometry. obtain the cla.ssical elastic tangent modulus of the material, it is necessary to solve the complete mechanics boundary-value problem that mathematically models the test configuratio n. To do this in detai 1taking into consideration the local geometry of the brai .n in the area of the measurements would represent a very difficult problem. However, if we make some simplifying assumptions, the problem becomes readily tractable. In particu lar, considering the size and local-radius of curvature of the brain in comparison with the area of the base of the transducer, it would seem reasonable to approximate the test configuration of the insertion of the transducer into the subpial region as the indentation of a viscoelastic material by a rigid, cylindrical, flat-ended punch. The solution to this problem is known for indentation in to an elastic half space and relates the total force on the punch to the insertion depth in terms of the size of the indentor and the elastic properties of the material [see, e.g., Green and Zerna (2)]. Thus, with the pressure-depth measurements from the elastic-response test and assuming a value for Poisson’s ratio, we can solve for the elastic modulus. The formulation used to relate the pressure-depth measurements, in the form of the ratio G, to the elastic modulus E is r,’ (1 - q2)
E= 2ri [l
- 41
- (r&+1
G
”
Here ri is the overall radius of the indentor, rt is the radius of the pressure transducer4 and 7 is Poisson’s ring
4 The difference that contains
in radii is due to the piston a nd the rigi d coplanar the pressure transducer (cf. Fig. 1).
In the experimental studies associated with this work, the short-time or elastic pressure-depth ratio seems to be a very sensitive and thus meaningful parameter for identifying certain aspects related to the condition of the brain. It is, as described, a (pseudo)elastic modulus (pressure-depth ratio) or (pseudo)compliance (depth-pressure ratio) in that the values measured reflect the test configuration as well as the system response. Nevertheless, we feel that these values determine more directly the brain mechanical properties, including brain compliance, than other techniques. For example, another interpretation of brain compliance is the value obtained as the slope of a volume-pressure curve obtained by injecting known amounts of fluid into the CSF space and recording the resulting rise in CSF pressure (6). Although these values represent an indication of the volumetric buffering capacity within the cranium, they reflect the superposed influence due to the elastic properties of the dural sac, the compressibility of the craniospinal vascular structures and the brain tissue. Moreover, controlled experimental studies on the effects of arterial tone changes, arterial blood pressure, and intracranial mass expansion on the CSF compliance have yielded inconsistent or conflicting results (4, 6). Further, in the methods described here the duraarachnoid membranes remain intact, and thus this is a noninvasive technique that can be considered for eventual clinical application. Hopefully, then, the influence of certain therapeutic regimens (e.g., osmotic diuretics, steroids, hyperventilation, etc.) on a swollen brain can be assesseddirectly by changes in the value of pressuredepth ratio (elastic modulus). In order to relate the values of pressure-depth ratio to the actual (classical) elastic (or tangent) modulus, it was necessary to approximate the model by a mechanics model for which the solution was known. Relating the present configuration to the problem of the penetration of an elastic half space by a rigid, flat, cylindrical punch, a range of values of the tangent modulus was obtained that was consistent with the values reported by Metz, McElhaney, and Ommaya (5) for in vivo tests of monkey brain. Although, from a mechanics point of view, the mechanics model approximation assumed by Metz, McElhaney, and Ommaya (5)” might appear to be a better configuration/model approximation than that r, In their study the authors made in vivo pressure-volume measurements with a small, inflatable, cylindrical rubber membrane attached to a hypodermic tubing and inserted into the brain tissue; they then modeled this as a uniform pressure applied to the interior of an infinitely thick-walled elastic cylinder.
Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
E. K.
1062 made here, the results from the two studies are comparable; however, the present technique, being noninvasive, has potential for clinical application. With regard to the linearity or nonlinearity of the elastic response of brain tissue, in their study Metz et al. reported a nonlinear elastic behavior in the sense that the modulus increased with increasing strain. Meanwhile, by reporting our results here with a straight-line best-fit representation of the experimental results, we are forcing a linear relationship between the pressure and depth (and thus stress and strain) response. Nevertheless, this was a good approximation in the tests reported here to pressures of about 40 mmHg. The differences undoubtedly reflect the influence of the approximation to the mechanics model at higher levels of stress (pressure, pumping pressure) and strain (insertion depth, fluid volume change).
WALSH
AND
A. SCHETTINI
Finally, we wish to reemphasize the fact that the direct determination of the in vivo pressure-depth ratio is an important parameter in characterizing the condition of the brain and in evaluating changes in that condition. The assumptions that lead to an evaluation of an elastic modulus are made only to relate the results to those reported in other investigations.
We acknowledge the able assistance of Mr. W. Furniss in obtaining much of the experimental data reported here. This work was supported by National Institutes of Health Grant 10381-02 and Veterans Administration Research Grant 7749-01. Address reprint requests to: Dr. A. Schettini, Surgical Division 691/112B, Veterans Administration Wadsworth Hospital Center, Los Angeles, Calif. 90073. Received
for publication
14 April
1975.
REFERENCES 1. GALFORD, J. E., AND J. H. MCELHANEY. A viscoelastic study of scalp, brain and dura. J. Biomech. 3: 211-221, 1970. 2. GREEN, A. E., AND W. ZERNA. Theoretic& Ekzsticity. Oxford: Clarendon Press, 1960, p. 176. 3. KOENEMAN, J. B. Viscoelastic Properties of Brain Tissue (MS Thesis). Case Institute of Technology, 1966. 4. MARMAROU, A., K. SHULMAN, AND J. LAMORGESE. A compartmental analysis of compliance and outflow resistance and the effects of elevated blood pressure. Intern. Symp. Intracranial Pressure, 2nd, Lund, Sweden, 1974. p. K-5. 5. METZ, H., J. MCELHANEY, AND A. K. OMMAYA. A comparison of the elasticity of live, dead, and fixed brain tissue. J. Biomech. 3:
453-458, 1970. 6. MILLER, J. D., P. J. LEECH, AND J. D. PICKARD. Volume pressure response in various experimental and clinical conditions. Intern. Symp. Intracranial Pressure, 2nd, Lund, Sweden, 1974. p. B-4. 7. SCHETTINI, A., AND E. K. WALSH. Pressure relaxation of the intracranial system in vivo. Am. J. Ph.ysioL. 225: 513-517, 1973. 8. SCHETTINI, A., AND E. K. WALSH. Experimental identification of the subarachnoid and subpial compartments by intracranial pressure measurements. J. Neurosurg. 40: 609-616, 1974. 9. WALSH, E. K., AND A. SCHETTINI. A pressure-displacement transducer for measuring brain tissue properties in vivo. J. Appl. Physiol. 38: 187-189, 1975.
Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
Elastic
OF
PHYSIOL~CY 1976. Prtnted
UI U.S.A.
behavior
of brain
tissue
in vivo
E. K. WALSH AND A. SCHETTINI University of Florida, Gainesville, Florida 32611; and Veterans Hospital Center, Los Angeles, California 90073
brain elastic response; pressure
brain
METHODS
tis-
AND IDENTIFICATION ofthe response behavior of the intracranial system is important for purposes of relating changes in the condition of the system, in particular the brain, to controlled variations, e.g., intracranial hypertension, inhalation of anesthetic agents, hyperventilation, etc. It is well known that brain tissue exhibits viscoelastic behavior (1, 3, 7); thus the mechanical response properties that identify the behavior include pressure relaxation, creep displacement, and the short-time or elastic response. This last property is particularly useful in a quantitative evaluation of that property usually described by the terms “soft” or “tight .” Here we describe a system for the measurement and evaluation of the elastic response of brain tissue in vivo through the intact dura. The experimental tests yield simultaneous pressure and displacement (insertion depth) measurements from which the elastic response or its inverse, the compliance, can be determined. The evaluation of the in vivo response properties of brain tissue, however, does require the certainty that the pressure-depth measurements are made in the subpial region. This determination is part of the experimental program involved in the elastic-response measurements and is described in RESULTS. The method differs significantly from that described previously by Schettini and Walsh (8). Finally, since the direct experi-
THE MEASUREMENT
Wadsworth
mental measurements represent an indication of the elastic behavior, rather than the classical elastic response modulus, we discuss a means of deriving the elastic modulus from the pressure-displacement measurements and compare these results with those reported elsewhere.
WALSH, E. K., AND A. SCHETTINI. EZastic behavior of brain tissue in vivo. Am. J. Physiol. 230(4): 1058-1062. 1976. -A measurement system and a test sequence have been developed to determine the in vivo elastic response of brain tissue in terms of a pressure-depth ratio. This parameter appears sensitive to changes in the tissue environment that may occur due to the influence of, e.g., anesthetic agents, hyperventilation, etc., and thus may be useful in evaluating such influences. The measurements are made with the dura-arachnoid membranes intact, thus maintaining the influence of the cerebrospinal fluid compartment on the response behavior of the brain tissue that comprises the subpial region. As an integral part of the test, the procedure also serves to determine the depth or position of the subpial region and thus assures that the subsequent pressure-depth measurements involve brain tissue response. Finally, some discussion is given to relating the measured pressure-depth ratio to the classical elastic modulus. Values of the pressure-depth ratio and the corresponding elastic modulus for seven dogs are given. bra in mechanical properties; sue compliance; intracranial
Administration
AND
PROCEDURE
Transducer and instrumentation. The transducer, shown schematically in Fig. 1, has been described at length elsewhere (9). Basically it involves a movableshaft system contained within a barrel that is firmly attached to a stainless steel collar implanted on the animal skull. The dura-arachnoid membranes are left intact; thus the influence of the cerebrospinal fluid on the measured system response is retained. A pressuresensitive element (type P-18 implantable transducer, Konigsberg Instruments, Inc., Pasadena, Calif.) is mounted in the base of the piston and secured by a rigid coplanar ring that serves to remove any measure of the tensile forces associated with the dura-arachnoid membranes. The displacement is measured by a linear variable-differential transformer (type 250-MHR LVDT, Schaevitz Engineering, Pennsauken, N. J.) whose core is mounted colinearly with the piston. Thus, the configuration of the instrument allows a rapid insertion of the pressure transducer into the intracranial cavity with a simultaneous recording of the pressure and the depth of insertion. The core-shaft collar can be preset to allow an initial displacement; then, advancing or withdrawing the depth-control cylinder provides controlled incremental changes in the insertion depth. Animal preparation. The measurements described here were made on dogs (15-25 kg) with the transducer mounted on a collar that had been implanted on a small burr hole (1.6 cm OD). The collar implantation was carried out with sterile techniques and general anesthesia, as described previously (7). Test procedure. Approximately 45 min before a test the animal was sedated lightly Innovar-Vet, 0.1 mg/kg iv). Additional sedation during the tests was provided by intermittent doses of thiopental (25-50 mg) given intravenously. Shortly before the test, the dog was placed in a reclining position and the transducer mounted to the implanted collar. The measurements were then made as follows: with the core-shaft collar fixed, the threaded depth-control cylinder, which serves to limit the depth of travel of the piston, was inserted into the transducer housing to a predetermined depth.
1058 Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
ELASTIC
RESPONSE
OF
BRAIN
Y-
TISSUE
IN
1059
VIVO
corresponding insertion depth, 8,, associated with the brain surface, i.e., the subpial region, prior to compression of the tissue within that region. In Fig. 2 the values of ps and 6, for dog 819 determined just prior to the elastic-response test are shown. In Fig. 3 the results of the elastic-response test shown
LVDT
core shaft
collar
depth control cylinder
barrel piston implan t collar A FIG.
1. Pressure-displacement
pressure transducer transducer.
Then the piston, and consequently the pressure-sensing transducer, was rapidly inserted (manually), causing a rise in pressure. The resulting pressure and depth were recorded on a graphic recorder. The piston was held at this insertion depth for approximately 2 s, then withdrawn, after which the system was allowed to recover for lo-15 min. Next the depth-control cylinder was repositioned a predetermined amount within the barrel, which resulted in a slightly greater insertion depth for the subsequent measurement. A sequence of such insertions, separated by periods of recovery, made up the elastic-response (compliance) test. Figure 2 shows the results of one such test (dog 619). The upper trace represents the transducer displacement and the lower trace the pressure response. The peak pressure versus the corresponding peak displacement yields the elastic response. These results for seven animals are discussed in the following section.
I 4
-- - ps ___- - - - __- _j - - - - - - - . I I L .
L v
Time FIG.
depth depth
.
.
i
.
L
.
L .
.
1
b 10 set
2. Elastic-response test for dog 819. Upper and lower trace is corresponding pressure; and pressure of subpial region.
trace is insertion 6, and pd identify
RESULTS
Elastic response (compliance). These tests were designed to determine the in vivo dynamic response of brain tissue, i.e., of the material in the subpial region of the intracranial system under the influence of a closed cerebrospinal fluid (CSF) compartment. It follows then that it was necessary to assure that the measurements attributed to the subpial material were indeed made in that region; i.e., the positions of the subregions of the system must be determined. This was done through a procedure developed by the present authors (8) and confirmed by an alternative method recently devised that is described in the next subsection. The results of these procedures yield the pressure, designated as pg. and
I
3 FIG.
values shown
3. Elastic-response of peak pressure in Fig. 2.
1
1
1
4
I
5
lnserrlon Depth - mm test results for dog 819. Circles and peak insertion depth for
Downloaded from www.physiology.org/journal/ajplegacy at Macquarie Univ (137.111.162.020) on February 15, 2019.
I
represent insertions
1060
E. K.
in Fig. 2 are presented with the values of the individual insertions indicated as the experimental points. In exhibiting these results we have taken pressure as the vertical scale and insertion depth as the horizontal. Thus the slope (or range of slope) Ap/A6 represents an elastic response or a (pseudo)elastic modulus.’ The inverse AS/Ap is an indication of the short-time or dynamic compliance and the value a (pseudo)compliance modulus. The break in the “curve” between the two ranges of nearly constant slope -identified as pS, 8, -is significant and is discussed in the next subsection. Of course the elastic response of the brain tissue is associated with the slope beyond the position 6,. However, since this position varies among animals, a more meaningful comparison of the elastic response of several animals is obtained if the graph of each is shifted so as to originate at the pointp,, & (thus, in essence, graphically subtractingp,, 6, from the values of pressure and depth for each insertion). This has been done for dog 619 in Fig. 4 along with the results of other tests, again with pressure as the vertical scale.’ To give a quantitative measure to the results we evaluate the slopes directly in terms of the parameter G,, = AplA6 in the units measured (mmHg/mm). The results for the tests shown in Fig. 4 are given in Table 1. In these tests great care was taken to maintain normal physiological conditions. Thus, from these results we consider the range of G, from approximately 15 to 25 mmHg/mm as the pressuredepth ratio for brain tissue under normal conditions. These values of pressure-depth ratio are useful directly in this form as a measure of the tissue response under normal conditions for comparison with similar values measured under controlled changes. However, in order to relate the results to measurements made with other configurations it is necessary to use the measured pressures and depths in the solution of the mechanics problem that approximates the experimental configuration. This is taken up in a later subsection. Determination Determination ofposition ofposition of subpial region from elastic-response test. In reference 8 a method was reported that used the results of tests with a controlled insertionrate pressure transducer to determine the position of the subpial region of the intracranial system that we identify as the brain surface. In that study a motor-controlled pressure transducer was used in tests that involved a uniform insertion of the pressure-sensing element at a constant rate to a depth corresponding to a predetermined pressure, followed by a uniform withdrawal. A detectable change in the pressure response was taken as an indication of a change in the material, i.e., a change in the system representing distinct regions of the intracranial system. Figure 5 shows the results of a test of constant insertion pressure on dog 819. The change in slope of the pressure response at an insertion depth of approximately 4.2 mm is taken to be I The reason for the appellation “pseudo” is discussed later in this section. z The single line in Fig. 4 for dog 819 represents an approximate best-fit to the experimental points (cf. Fig. 3), as was done for the other tests.
?
I
I
1
1 .5
WALSH
I
AND
A. SCHETTINI
I
I
I I.0
1
*
1
a IO
01 0
1
b-b, 4. Results represent best-fit FIG.
I 1.5
1
-mm
of elastic-response tests in 7 dogs. Sloping approximations to experimental points.
lines
1. Mechanical para meters of brain tissue elastic response in 7 dogs
TABLE
G,, mmHg/mm
DOC: 819 770 854 811 828 784 885 Mean + SD * Based
on model
E *, x 10’ dynes/cm’
2.80 3.01 3.01 3.10 3.30 4.01 4.12 3.3 ?I 0.52
17.3 18.6 18.6 19.2 20.4 24.8 25.5 20.6 + 3.2 and assumptions
discussed
in
RESULTS.
the position of the brain surface3 at the time of this particular test. As one might expect, this determination can also be made from the results of the elastic-response test. That is, since the hypothesis is that the incremental change in pressure associated with an incremental change in insertion depth is a measure of the elastic response of the material in the region where the measurements are made, then it would be expected that this ratio would change as the pressure transducer moved from one region to the other. Thus, in the present configuration, if the initial insertions are carried out within the CSF-transition regions and subsequent insertions within the subpial region, we would expect to see a difference in the pressure-depth ratios associated with each. Figure 3 shows such a change in slope with the point of change labeled as pwq,6,. -Here &is approximately 4. 0 mm. A.lthough this corn.pares to the value obtained from the pressure test to within the experi3 We define the position which subsequent insertion of the subpial region.
of the brain surface as that depth beyond involves compression of the brain tissue
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ELASTIC
RESPONSE
OF
BRAIN
TISSUE
IN
1061
VIVO 6
5
I” E z” E
ratio. The value assumed for 7 was 0.5 (5). With G, in units of millimeters of Hg per millimeter and the radii in units of millimeters, E is in units of millimeters of Hg. Converting this to dynes per square centimeter, the range of values of G, in Table 1 corresponds to moduli of 2.8-4.1 x 10” dynes/cm? This compares with a value of 2 x 10:) dynes/cm2 reported by Metz, McElhaney, and Ommaya (5) for the lowest values of strain in their tests. DISCUSSION
0
Time FIG.
onset
5. Pressure test for dog of subpial region (see text).
-
min
819.
Region
marked
6, indicates
mental accuracy of +O. 1 mm insertion depth, there may also have occurred a slight shift in position during the time between the pressure test and the elastic-response test. from pressureDetermination of elastic modulus The results of th .e pressure-depth depth measurements,
measurements yield a slope or pressure-depth ratio that not only reflects the elastic response of the subpial terial but also the test confi .guration and geometry. obtain the cla.ssical elastic tangent modulus of the material, it is necessary to solve the complete mechanics boundary-value problem that mathematically models the test configuratio n. To do this in detai 1taking into consideration the local geometry of the brai .n in the area of the measurements would represent a very difficult problem. However, if we make some simplifying assumptions, the problem becomes readily tractable. In particu lar, considering the size and local-radius of curvature of the brain in comparison with the area of the base of the transducer, it would seem reasonable to approximate the test configuration of the insertion of the transducer into the subpial region as the indentation of a viscoelastic material by a rigid, cylindrical, flat-ended punch. The solution to this problem is known for indentation in to an elastic half space and relates the total force on the punch to the insertion depth in terms of the size of the indentor and the elastic properties of the material [see, e.g., Green and Zerna (2)]. Thus, with the pressure-depth measurements from the elastic-response test and assuming a value for Poisson’s ratio, we can solve for the elastic modulus. The formulation used to relate the pressure-depth measurements, in the form of the ratio G, to the elastic modulus E is r,’ (1 - q2)
E= 2ri [l
- 41
- (r&+1
G
”
Here ri is the overall radius of the indentor, rt is the radius of the pressure transducer4 and 7 is Poisson’s ring
4 The difference that contains
in radii is due to the piston a nd the rigi d coplanar the pressure transducer (cf. Fig. 1).
In the experimental studies associated with this work, the short-time or elastic pressure-depth ratio seems to be a very sensitive and thus meaningful parameter for identifying certain aspects related to the condition of the brain. It is, as described, a (pseudo)elastic modulus (pressure-depth ratio) or (pseudo)compliance (depth-pressure ratio) in that the values measured reflect the test configuration as well as the system response. Nevertheless, we feel that these values determine more directly the brain mechanical properties, including brain compliance, than other techniques. For example, another interpretation of brain compliance is the value obtained as the slope of a volume-pressure curve obtained by injecting known amounts of fluid into the CSF space and recording the resulting rise in CSF pressure (6). Although these values represent an indication of the volumetric buffering capacity within the cranium, they reflect the superposed influence due to the elastic properties of the dural sac, the compressibility of the craniospinal vascular structures and the brain tissue. Moreover, controlled experimental studies on the effects of arterial tone changes, arterial blood pressure, and intracranial mass expansion on the CSF compliance have yielded inconsistent or conflicting results (4, 6). Further, in the methods described here the duraarachnoid membranes remain intact, and thus this is a noninvasive technique that can be considered for eventual clinical application. Hopefully, then, the influence of certain therapeutic regimens (e.g., osmotic diuretics, steroids, hyperventilation, etc.) on a swollen brain can be assesseddirectly by changes in the value of pressuredepth ratio (elastic modulus). In order to relate the values of pressure-depth ratio to the actual (classical) elastic (or tangent) modulus, it was necessary to approximate the model by a mechanics model for which the solution was known. Relating the present configuration to the problem of the penetration of an elastic half space by a rigid, flat, cylindrical punch, a range of values of the tangent modulus was obtained that was consistent with the values reported by Metz, McElhaney, and Ommaya (5) for in vivo tests of monkey brain. Although, from a mechanics point of view, the mechanics model approximation assumed by Metz, McElhaney, and Ommaya (5)” might appear to be a better configuration/model approximation than that r, In their study the authors made in vivo pressure-volume measurements with a small, inflatable, cylindrical rubber membrane attached to a hypodermic tubing and inserted into the brain tissue; they then modeled this as a uniform pressure applied to the interior of an infinitely thick-walled elastic cylinder.
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E. K.
1062 made here, the results from the two studies are comparable; however, the present technique, being noninvasive, has potential for clinical application. With regard to the linearity or nonlinearity of the elastic response of brain tissue, in their study Metz et al. reported a nonlinear elastic behavior in the sense that the modulus increased with increasing strain. Meanwhile, by reporting our results here with a straight-line best-fit representation of the experimental results, we are forcing a linear relationship between the pressure and depth (and thus stress and strain) response. Nevertheless, this was a good approximation in the tests reported here to pressures of about 40 mmHg. The differences undoubtedly reflect the influence of the approximation to the mechanics model at higher levels of stress (pressure, pumping pressure) and strain (insertion depth, fluid volume change).
WALSH
AND
A. SCHETTINI
Finally, we wish to reemphasize the fact that the direct determination of the in vivo pressure-depth ratio is an important parameter in characterizing the condition of the brain and in evaluating changes in that condition. The assumptions that lead to an evaluation of an elastic modulus are made only to relate the results to those reported in other investigations.
We acknowledge the able assistance of Mr. W. Furniss in obtaining much of the experimental data reported here. This work was supported by National Institutes of Health Grant 10381-02 and Veterans Administration Research Grant 7749-01. Address reprint requests to: Dr. A. Schettini, Surgical Division 691/112B, Veterans Administration Wadsworth Hospital Center, Los Angeles, Calif. 90073. Received
for publication
14 April
1975.
REFERENCES 1. GALFORD, J. E., AND J. H. MCELHANEY. A viscoelastic study of scalp, brain and dura. J. Biomech. 3: 211-221, 1970. 2. GREEN, A. E., AND W. ZERNA. Theoretic& Ekzsticity. Oxford: Clarendon Press, 1960, p. 176. 3. KOENEMAN, J. B. Viscoelastic Properties of Brain Tissue (MS Thesis). Case Institute of Technology, 1966. 4. MARMAROU, A., K. SHULMAN, AND J. LAMORGESE. A compartmental analysis of compliance and outflow resistance and the effects of elevated blood pressure. Intern. Symp. Intracranial Pressure, 2nd, Lund, Sweden, 1974. p. K-5. 5. METZ, H., J. MCELHANEY, AND A. K. OMMAYA. A comparison of the elasticity of live, dead, and fixed brain tissue. J. Biomech. 3:
453-458, 1970. 6. MILLER, J. D., P. J. LEECH, AND J. D. PICKARD. Volume pressure response in various experimental and clinical conditions. Intern. Symp. Intracranial Pressure, 2nd, Lund, Sweden, 1974. p. B-4. 7. SCHETTINI, A., AND E. K. WALSH. Pressure relaxation of the intracranial system in vivo. Am. J. Ph.ysioL. 225: 513-517, 1973. 8. SCHETTINI, A., AND E. K. WALSH. Experimental identification of the subarachnoid and subpial compartments by intracranial pressure measurements. J. Neurosurg. 40: 609-616, 1974. 9. WALSH, E. K., AND A. SCHETTINI. A pressure-displacement transducer for measuring brain tissue properties in vivo. J. Appl. Physiol. 38: 187-189, 1975.
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