Pulsatile Flow Through a Bifurcation With a Cerebrovascular Aneurysm

Transcription

1 Tong-Miin Liou Professor. Tzung-Wu Chang Graduate Student. Wen-Chin Chang Graduate Student. Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China Pulsatile Flow Through a Bifurcation With a Cerebrovascular Aneurysm Laser-Doppler velocimetry measurements and flow visualization were complementarity made in pulsatile and steady flow in a cerebrovascular aneurysm model with bifurcation angles of 60, 90, and 140 deg, and volume-flow rate ratios between the branches of 1 to and 3 to 1. The mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 600, 800, and 280, respectively. For uneven branch flow, it is found that the flow activity inside the aneurysm and the stresses acting on the aneurysmal wall increase with increasing bifurcation angle. More importantly, the present angle suggests the presence of a critical bifurcation angle below which the aneurysm is prone to thrombosis, whereas above which the aneurysm is susceptible to progression or rupture. For evenly distributed branch flow, the intra-aneurysmal flow is sluggish and therefore prone to thrombosis for all studied bifurcation angles. ntroduction Arterial diseases, such as thrombosis formation, thinness of the vascular walls, and aneurysmal progression or rupture may be related to the flow structure in a cerebrovascular aneurysm (Figs. 1 and 2). n general, the intra-aneurysmal flow pattern and the flow velocities mainly vary with the flow ratio between the branches of the bifurcation and with the bifurcation angle. This paper will aim at investigating these two major effects on the local flow structure in cerebrovascular aneurysms. Glass aneurysm models and dye flow visualization have been extensively used to study the flow structures in this area. Ferguson (1970 and 1972) postulated a biophysical hypothesis for the initiation, growth, and rupture of intracranial aneurysms based on the patterns of both steady and pulsatile flow observed by dye injection and on the clinical phonocatheter studies. By dye injection Roach et al. (1972) found that the critical Reynolds number at which turbulence developed in glass model bifurcation depended on the angle of bifurcation. Steiger and Reulen (1986) performed flow visualization in glass model aneurysms and intra-operative Doppler recordings on patients. They reported that all observed irregularities of flow were in zones of deceleration. Using dye injection and streaming double refraction, Steiger et al. (1987) further studied the basic flow structure in model saccular aneurysms. Stagnation of flow at the neck and little intra-aneurysmal circulation were found with terminal aneurysms of the basilar bifurcation type if the outflow through the branches was symmetric. They found that the use of pulsatile perfusion did not significantly alter the basic flow patterns observed with steady flow. Computation- ally, Perktold et al. (1989) proceeded the finite element simulation of pulsatile non-newtonian and Newtonian blood flows in a straight terminal aneurysm and found that for the considered large artery model only minor difference existed between calculated non-newtonian and Newtonian flow patterns. Steiger's computer simulation (1992) concluded that initially spherical aneurysms, sausage-shaped aneurysms, and discshaped aneurysms all grew toward a spherical contour and that HEAD TANK COMPUTER OSCLLOSCOPE PROBE FBER JUNCTON COUNTER PROCESSOR 6) DOWNMXER ) PHOTOMULTPLER ) OPTCAL FBER 9) AT*" Laser W) OPTCS Contributed by the Bioengineering Division for publication in the JOURNAL OF BOMECHANCAL ENONEERNG. Manuscript received by the Bioengineering Division April 29, 1992; revised manuscript received March 29, Associate Technical Editor: K. Hayashi. Fig. 1 Schematic drawing of overall experimental system 112 / Vol. 116, FEBRUARY 1994 Transactions of the ASME Copyright 1994 by ASME

2 46 Unit:mm 9b L a = 80 b=46 c=46 d = 60 Region : Bifurcation Region E: Aneurysm Zone Fig. 2 Sketch of configuration, coordinate system, and dimensions of cerebrovascular aneurysm models compound aneurysms consisting of two spheres remained complex. Quantitatively, Steiger et al. (1988) performed laser-doppler velocimetry (LDV) measurements of flow velocities in a straight terminal aneurysm situated in the axis of the afferent vessel and in an angled terminal aneurysm arising at a 45 deg relative to the plane of the parent bifurcation. Both glass and silastic models were used and the tested Reynolds number was of 500. Their results showed that elasticity had only a minor influence on the average flow velocities. Using the same test models, Liepsch et al. (1991) further found that the geometrical relation between aneurysm and parent vessel was the primary factor governing intra-aneurysmal flow pattern and that the elasticity of the model wall did not affect the global turnover rates but it damped the intra-aneurysmal pulse wave. Although the above in vitro studies have clarified some hemodynamic effects, in vivo investigations are also important since the aneursymal development and growth are considered to be closely related to local vascular wall properties and structure (Forbus, 1930; Glynn, 1940; and Stehbens, 1962) in addition to hemodynamic factors. Suzuki and Ohara (1978) in their clinicopathological study of origin, rupture, repair and growth of the cerebral aneurysms reported that the walls of large aneurysms were usually thicker, but parts of the neck and sac might vary in thickness. Sekhar and Heros (1981) gave a fine review of medical defect theory, elastic lamellar theory, degenerative theory, and other congenital theories relevant to the origin of saccular aneurysms. Recently, Kim and Cervos- Navarro (1991) studied the relative importance of two main factors in the pathogenesis of saccular aneurysms: degenerative changes of the internal elastic laminar and the defect or the gap in the medial muscle layer, and found that the former factor played a main role in the development of the spontaneous saccular cerebral aneurysm in a rat. The information provided by the aforementioned works is valuable; nevertheless, more quantitative investigations, especially the effects of the bifurcation angle and flow rate ratio between the branches on the flow structure in the cerebrovascular aneurysm, are obviously needed for a better understanding of the relation between fluid dynamic behavior and arterial disease. The purpose of the present work is, therefore, to characterize the pulsatile flowfield in straight cerebrovascular aneurysms with various bifurcation angles in terms of mean velocity and fluctuating components using non-invasive LDV techniques. Moreover, the measured results will be complemented by a flow visualization study for different branch flow rate ratios. t is hoped that the obtained data set will also be useful for validating theoretical models. Furthermore, the adequacy of using steady flow to simulate pulsatile blood flow in model saccular aneurysms will be evaluated. Test System and Conditions Test System. The whole test system including the optical system and the pulsatile flow system is shown schematically in Fig. 1. The LDV optics was set up in a dual-beam back scattering optical fiber configuration with a 300-mW argon ion laser (514.5-nm wavelength) as the coherent light source. This beam was split into two parallel beams of equal intensity by a beamsplitter. A Bragg cell was used to cause 40 MHz frequency shift on one of the beams. A frequency shift is used to eliminate the directional ambiguity. The resulting pair of beams was then directed into two single-mode polarizationpreventing fibers. Within the fiber optic probe, the laser beams from the two fibers were collimated and passed through a 102- mm focal-length lens. The focused beams entered the test section through the transparent Pyrex glass wall, intersected inside the model giving a probe volume with dimensions of 8 mm by 1.26 mm. The fiber optic probe was mounted on a small milling machine with four vibration mounts, allowing the probe volume to be positioned with 1 mm resolution. The light scattered from the seeding particles was collected by the aforementioned lens and a receiving lens and focused onto one multimode receiving fiber for delivering the scattered light to a photomultiplier. The detected signal was electrically downmixed to the appropriate frequency shift of 20 KHz. Then a counter processor with 1 ns resolution was used to process the Doppler signal and feed the digital output to a PC/AT for storage and analysis. Plastic painting solution was mixed and filtered (Fig. 1) to give seeding particles in the size range up to 1 fim. A rotary pump (Little Giant LG300 tygon tubing) was used to produce a pulsatile flow with a wave form similar to that of a sine wave, as shown in Fig. 3. As the flow was established, it was delivered to the test section through a rotameter, a flow straightener and five screens in the settling chamber, and a bell-shaped 5:1 contraction. Downstream of the test section, a = b = c = D = d = Hz = L = aneurysm height distance from orifice to fundus orifice diameter afferent conduit diameter fundus diameter frequency unit = cycle/second length of bifurcation zone Re U u m u X* Reynolds number = U'D/v streamwise mean velocity streamwise bulk mean velocity streamwise fluctuating intensity normalized streamwise coordinate: X* >0: X* =X/a; X*<0:X*=X/L Y* = normalized transverse coordinate: Y* = Y/D Z* = normalized spanwise coordinate: Z* = Z/D v - kinematic viscosity 6 b = angle of bifurcation d c = critical bifurcation angle Journal of Biomechanical Engineering FEBRUARY 1994, Vol. 116/113

3 steady peak minimal &4 Second Fig. 3 Volume-flow rate during pulsation at X* = and a mean Reynolds number of 600 return flow from the dump tank to the head tank was provided by a pump. The instantaneous flow rates of the vessels were measured by electro-magnetic flowmeters (EMF) (Rosemount, Model 8722) located downstream of the test section. Test Models and Conditions. The configuration of the test model, coordinate system, and dimensions are presented in Fig. 2. The test section was made of 2-mm Pyrex glass. The afferent duct and symmetric daughter ducts, respectively, had the inner diameter of 46 mm and 32 mm, and were 1680-mm and 150-mm long. The diameter of the aneurysmal orifice was equal to that of the afferent duct. The distance between orifice and fundus measured one time the diameter of the orifice and the diameter of the fundus was by a factor of 1.3 larger than that of the orifice. The LDV velocity measurements were mainly carried out along two orthogonal planes, Y* = 0 and Z* = 0 (Fig. 2), and were made at 6 to 9 axial stations. n each station the measurements were taken at 13 to 17 locations. The test fluid was water with a viscosity of 02 cp and density of g/cm 3. Pulsatile flow was produced at a rate of 78 beats/min or at a Womersley number of 26. The tested mean, peak, and minimal Reynolds numbers in the parent vessel were 600, 800, and 280, respectively. The parent bifurcations were axisymmetric with 60, 90, and 140 deg angles between the branches. For comparison purpose, the asymmetric flow ratio between the branches of the bifurcation was selected to be 75%:25% that had been adopted by Steiger et al. (1988). Results and Discussion The mean velocity was calculated from the probability distribution function of the measurements which were typically taken from 4096 cycles during maximal or minimal flow phase of the cycle. The statistical errors in mean velocity and fluctuation intensity were less than 1.8 and 2.2 percent, respectively, for a 95 percent confidence level. A constant time interval sampling mode was used to correct velocity bias. Mean Flow Pattern. Figure 4 depicts the stream wise evolution of dimensionless axial mean-velocity profiles along Y* = 0 and Z* = 0 planes in the parent vessel and cerebrovascular aneurysm for a bifurcation angle of 140 deg during both steady (solid line) and pulsatile flow. For pulsatile flow the axial mean-velocity profiles presented in Fig. 4 are during peak flow (circle symbol) and minimal flow (triangle symbol). n general, the overall trends exhibited by the pulsatile flow velocity distributions are similar to those revealed by the steady flow although they differ somewhat in detail. For the plane Z* = 0, all the mean velocity profiles are quite symmetric to the central axis and the velocity decays toward aneurysm fundus. The retardation of aneurysm fundus makes the velocity profiles inflected near the vessel wall (Y* = ±0.5). Flow reversals resulted from the instability associated with inflection points in the velocity profiles occur firstly for the minimal flow (e.g., X s =-2.48) and then for the steady flow (e.g., X* = -). Further downstream at aneurysm neck (X* = ) flow reversals even occur during maximal flow with maximum negative velocities as high as 71 percent of U,. t may be noted that both steady and pulsatile flow have flow reversals and maximum mean-velocity gradients at aneurysm neck since as Fig. 4 Streamwise evolution of dimensionless axial mean-velocity profiles along V* = 0 and Z* = 0 plane for 0 6= 140 deg during both steady and pulsatile flow the fluids flow into the aneurysm they are immediately and significantly decelerated by the aneurysm fundus. The fluid motion inside the aneurysm in the Z* = 0 plane is practically stagnant. n contrast, for the plane Y* = 0 both steady and pulsatile flow profiles are asymmetric and skewed toward the dominant branch (75 percent outflow). The unevenly distributed branch flow induces a forced-vortex like intra-aneurysmal flow with inflow near the dominant branch and outflow near the branch with the smaller flow, an active flow distinctly differing from the sluggish flow observed for the symmetric outflow case (Kerber et al., 1983 and Steiger et al., 1987). t should be mentioned that the present work has been restricted to an axisymmetrical aneurysm. For the case of a nonaxisymmetrical aneurysm, the flow characteristics may be different from that described in the present work. An example is an asymmetrical bifurcation with a side branch arising at a 90 deg angle from a straight parent vessel and the aneurysm is situated between the side branch vessel and the downstream main conduit. For this case, and if the flow through the side branch is higher than 50 percent of the total afferent flow, the main inflow filling the aneurysm undulates near the downstream lip of the orifice, i.e., near the main conduit with the smaller flow, and propagates into the fundus in waves (Steiger and Reulen, 1986). This behavior is opposite to the present case with inflow near the dominant branch. Generally, the flow structure in the Z* = 0 plane observed for the case of 6 b = 140 deg is similarly exhibited by the cases of d b = 90 deg and 6 b = 6Q deg. However, the flow pattern in the Y* - 0 plane varies with 6 b. The results for the case of 8 b = 60 deg are selected and plotted in Fig. 5, which presents a striking contrast to those shown in Fig. 4. t is seen that the uneven branch flow has a rather weak effect (e.g., X* = 0.25) on the intra-aneurysmal flow pattern of 6 b = 60 deg. As a matter of fact, the intra-aneurysmal flow is sluggish in both Y* = 0 and Z* = 0 plane for the 6 b = 60 deg case. t may be instructive to compare the mean velocity profiles at aneurysm neck (X* =0) with those at the aneurysm center (X* =0.5), as depicted in Fig. 6. The purpose is to examine that the effect of 114 / Vol. 116, FEBRUARY 1994 Transactions of the ASME

4 25% Flow Condition 75% steady peak minimal 6tr6cf plane: Y*= (bifurcation zone) U _ Flow ^D/. Condition plane: Y*= - - X*= 75% 6b=60 u % steady peak minimal Flow Condition X*= % e b =6o plane: Y*= (intra-aneurysm) X*=0.5 1,0 y Um - - X*=0.25 J L. -0, z* Fig. 5(b) 0.5 H Fig. 5 Streamwise evolution of dimensionless axial mean-velocity profiles along V* = 0 plane for 0 b = 60 deg during both steady and pulsatile flow uneven branch flow is maintained or reduced as the fluids flow from aneurysm neck into center for the investigated range of 9 b. Among the three investigated bifurcation angles, Fig. 6 shows that only for 6 b = 140 deg the skew mean velocity profiles at aneurysm neck can induce sufficiently strong forced-vortex like rotation inside the aneurysm in the Y* = 0 plane. n fact, Fig. 6 may suggest that there exists a critical bifurcation angle d c between d b = 90 deg and 0 6 =14O deg. Below the critical bifurcation angle the uneven branch flow is unable to induce significant well-directed rotational flow inside the saccular aneurysm. Cerebrovascular aneurysms for 6b<8 c are therefore prone to thrombosis due to the sluggish intra-aneurysmal flow. Above the critical bifurcation angle the well-directed forcedvortex like rotation inside the aneurysm results in large mean- 1.5 U l.o 1.5 U 1-0 TJ Um - 25% plane:y* = *- X*= --»-- X*=0.5 25% plane:y*= -9-X*= -*-X*=0.5 Flow Condition 75% eb=9o minimal peak steady,25 Z* J L_ 0.25 Fig. 6(b) Flow Condition 75% 9 b =140 minimal peak o.o - U Um Fig. 6(c) Fig. 6 Dimensionless axial mean velocity profiles at aneurysm neck and center for (a) 6 b = 60 deg, (b) 6 b = 90 deg, (c) 0 b = 140 deg during both steady and pulsatile flow Journal of Biomechanical Engineering FEBRUARY 1994, Vol. 116 /115

5 Fig.7(b) Fig.7(a) velocity gradients and, in turn, large shear stresses near the aneurysmal wall and may be responsible for the thinness of the aneurysmal wall. This observation, together with the fact that large shear stresses occur at aneurysm neck as shown in Fig. 4, may imply that susceptibility of saccular aneurysms to progression or rupture for fh> Oc' There is one more aspect worth to be addressed here. The present in vitro study of pulsatile and uneven branch flow depicts the occurrence of the maximum mean-velocity gradients and, hence, the largest shear stresses near or at the aneurysm neck for all three studied bifurcation angles. Our in vitro result parallels the in vivo result of Suzuki and Ohara (1978) who measured the thickness of the neck and the dome in 23 unruptured aneurysms and found that the neck was thinner than the dome in the majority of instances. Using frame-by-frame analysis of the motions and paths of the latex particles, Nakatani et al. (1991) also roughly estimated the shear stress was highest near the aneurysm neck in rats. As a complement as well as a check of the above LDV measured results, a dye-injection flow visualization was performed to observe the flow patterns in the y* = 0 plane for both unevenly and evenly distributed branch flow and for the studied three bifurcation angles. The resultant photographs are shown in Figs. 7 and 8. t is seen that for uneven branch flow only for Ob = 140 deg the dye streak line exhibits a forcedvortex rotation inside the aneurysm and Fig. 8 clearly supports the existence of a critical bifurcation angle between Ob = 90 deg and Ob= 140 deg, as suggested by the LDV measurements. For even branch flow, the flow is rather sluggish for all studied bifurcation angles. Also note that the flow patterns in the branch duct, Fig. 7 and Fig. 8, are helical shape induced by flow curvature. Fig.7(c) Fluctuating Motion. Figure 9 shows the development of fluctuating intensity along the central axis for the investigated Flg.7 Photographs of flow visualization under the case of even branch flow for (8) 80 = 60 deg. (b) 80 = 90 deg, and (c) 80 = 140 deg during steady flow 116/ Vol. 116, FEBRUARY 1994 Transactions of the ASME

6 Fig.8(e) Fig. 8 Photographs of flow visualization under the case of uneven branch flow for (a) 8~ = 60 deg, (b) 8~ = 90 deg, and (c) 8b = 140 deg during steady flow steady Fig.8(a) u' peak. minimal b=6(fA, y' ~ / u' O. 4. J?, \ \ / l \ 0.2 \ \...,.~ <;),',, \,, '',: 0.8, u' 0.6,, / 0.4 \,, ' ' '' ' : ;' 0.2 / ~ ;.>-....f Fig.8(b) bifurcation angles during both steady and pulsatile flow. For pulsatile flow during both peak and minimal flow rate, the maximum fluctuating intensities all occur at aneurysm neck (X' = 0, Fig. 9) since across aneurysm neck the flow is drajournal of Biomechanical Engineering x* 0,0 0.5 Fig. 9 The distributions of fluctuating intensity along the central axis for 8b = 60 deg, 90 deg, and 140 deg during both steady and pulsatile flow matically decelerated. That is, in a flow with a negative velocity gradient (au/ax<o, retarded flow in space), the tendency is toward an increase in fluctuation (a positive fluctuation production term: - (u' )2au/ax> 0). That fluctuating intensity FEBRUARY 1994, Vol. 116/117

7 increases with deceleration shown in Fig. 9 is consistent with that all observed irregularities of flow were in the zones of deceleration reported previously by Steiger and Reulen (1986) based on the model flow visualization and intra-operating Doppler recording on patients. These meaured fluctuations also confirm Ferguson's clinical phonocatheter study (1972) in which audible bruits were recorded from the sacs of 12 of 19 intracranial aneurysms studied at the time of craniotomy. Among the three studied bifurcation angles, d b = 140 deg generates the largest fluctuating intensity with a value as high as 110 percent of U m due to the steepest velocity gradient associated with the transformation of the skew velocity profile into the forcedvortex intra-aneurysmal rotation. For the case of steady flow, Fig. 7 shows that the regions where large fluctuating intensities prevail occur somewhat upstream of aneurysm neck for smaller bifurcation angles. As the bifurcation angle increases from 6 b = 60 deg to 0 fi = 140 deg, the position of the maximum fluctuating intensity moves from about first half of bifurcation zone toward the aneurysm neck and the value increases from about 30 percent of U, to 60 percent of U,. Because fluctuation usually results in a significant mechanical stress and structural fatigue of the vascular wall (Ferguson, 1972) and the results presented above (both pulsatile and steady flow) all indicates that the aneurysm neck is acted by the maximum fluctuating intensity as long as 8 b >6 c, the studied 6 b = 140 deg case is most prone to aneurysmal progression. Conclusions The following conclusions are drawn from the data presented: 1 For unevenly distributed branch flow under both pulsatile and steady condition, the present LDV measurements and flow visualization suggest the presence of a critical bifurcation angle between 0 b = 90 deg and d b = 140 deg above which the intraaneurysmal flow activity in the Y* = 0 and Z* = 0 plane is characterized by the forced-vector rotation and sluggish motion, respectively, whereas below which the flow is practically stagnant inside the aneurysm for all studied bifurcation angles. This behavior has not been reported previously and poses a challenge problem for computational models. 2 For all tested cases the cerebrovascular aneurysm is prone to thrombosis due to sluggish flow inside the aneurysm, except that for 6 b = 140 deg under uneven branch flow-rate ratio the intra-aneurysmal vortex structure tends to cause thinness of the aneurysm wall or aneurysmal progression. 3 For pulsatile and uneven branch flow the maximum meanvelocity gradients and fluctuating intensities, i.e., maximum stresses and resulting fatigue, are found to be near aneurysm neck for all investigated bifurcation angles. 4 As far as the mean flow pattern is concerned, using steady flow to simulate pulsatile flow in model cerebrovascular aneurysms is found to be qualitatively adequate. For fluctuating motion, however, some discrepancies relevant to the fluctuating amplitude and the region where maximum fluctuation prevails are found between pulsatile and steady flow. Acknowledgment Support for this work was provided by the Veterans General Hospital and National Tsing Hua University under the contract of VGHTH References Ferguson, G. G., 1970, "Turbulence in Human ntracranial Saccular Aneurysms," J. Neurosurg., Vol, 33, pp Ferguson, G. G., 1972, "Physical Factor in the nitiation, Growth, and Rupture of Human ntracranial Saccular Aneurysm," J. Neurosurg., Vol. 37, pp Forbus, W. D., 1930, "On the Origin of Miliary Aneurysms of the Superficial Cerebral Arteries," Bull. Johns Hopkins Hosp., Vol. 478, pp Glynn, L. E., 1940, "Medial Defects in the Circle of Willis and Their Relation to Aneurysm Formation," J. Pathol. Bacterial, Vol. 51, pp Kerber, C. W., and Heilman, C. B., 1983, "Flow in Experimental Berry Aneurysms: Method and Model," AJNR, Vol. 4, pp Kim, C, and Cervos-Navarro, J., 1991, "Spontaneous Saccular Cerebral Aneurysm in a Rat," Acta Neurochir., pp Liepsch, D., Poll, A., and Steiger, H. J., 1991, "Fluid Dynamic Studies in Terminal Aneurysms," Medical & Biological Engineering & Computing, Vol. 29 Supplement, p. 19. Nakatani, H., Hashimoto, N., Kang, Y., Yamazoe, N., Kikuchi, H., Yamaguchi, S., and Niimi, H., 1991, "Cerebral Blood Flow Patterns at Major Vessel Bifurcations and Aneurysms in Rats," /. Neurosurg., Vol. 74, pp Perltold, K., Peter, R., and Resch, M., 1989, "PulsatileNon-Newtonian Blood Flow Simulation Through a Bifurcation with an Aneurysm," Biorheology, Vol. 26, pp Roach, M. R., Scott, S., and Ferguson, G. G., 1972, "The Hemodynamic mportance of the Geometry of Bifurcations in the Circle of Willis (Glass Model Studies)," Stroke, Vol. 3, pp Sekhar, L. N., and Heros, R. C, 1981, "Origin, Growth, and Rupture of Saccular Aneurysms: A Review," Neurosurgery, pp Stehbens, W. E., 1962, "Cerebral Aneurysms and Congenital Abnormalities," Australas. Ann. Med., Vol. 11, pp Steiger, H. J., and Reulen, H.-J., 1986, "Low Frequency Flow Fluctuations in Saccular Aneurysms," Acta Neurochir., Vol. 83, pp Steiger, H. J., Poll, A., Liepsch, D., and Reulen, H.-J., 1987, "Basic Flow Structure in Saccular Aneurysms: A Flow Visualization Study," Heart and Vessels, Vol. 3, pp Steiger, H. J., Poll, A., Liepsch, D., and Reulen, H.-J., 1988, "Hemodynamic Stress in Terminal Aneurysms," Acta Neurochir., Vol. 93, pp Steiger, H. J., 1991, "Growth of Cerebral Saccular Aneurysms," Medical & Biological Engineering & Computing, Vol. 29 Supplement, p. 19. Suzuki, J., and Ohara, H., 1978, "Clinicopathological Study of Cerebral Aneuryms: Origin, Rupture, and Growth," J. Neurosurg., Vol. 48, pp / Vol. 116, FEBRUARY 1994 Transactions of the ASME