- Email: [email protected]
Biophysical aspects of the intracranial circulation
Review
Biophysical
aspects
of the intracranial
circulation
Yu. E. Moskalenko Yu. Ya. Kislyakov G. B. Vainshtein B. B. Zelikson Leningrad, U.S.S.R.
T
he biophysical structure of intracranial hemodynamics is determined primarily by the structural features distinguishing the vascular system of the brain and of the cerebrospinal cavity as a whole. Foremost among these is the limitation of the capacity of the cranial cavity, which is responsible for the complex character of the relationships between volumes and pressures of the fluid media-arterial and venous blood, cerebrospinal fluid (CSF)-inside the closed skull. The relationships between volumes and pressures of the blood in the cranial and vertebral cavities, effected through the flow of CSF to and fro between them, are another important consideration. With existing techniques, it is possible to record the cerebral blood flow accurately only by means of the Kety-Schmidt method, with its high inertia, or by variations of this method. The basic biophysical parameters of the intracranial hemodynamics (intracranial blood volume, intracranial pressure) are recorded by relatively simple and exceedingly dynamic
methods.’ Data concerning changes in these parameters also are interesting because, unlike data for the volume of the cerebral blood flow, they can indicate rapid changes in the intracranial circulatory system blood flow, and provide some information about the “stress” placed on the control system of the intracranial circulation and of its powers of compensation. However, the absence of any unanimously accepted concept of the biophysical structure of the intracranial circulatory system has led, at the present time, to the accumulation of many facts that are difficult to explain-facts which complicate still further the already confused notions concerning the function of this important physiological system. Therefore, we will attempt in this paper to organize the accumulated data of our investigations on the biophysics of the intracranial circulation. We will propose a hypothesis of the biophysical structure of cerebral circulation, which will contribute to the understanding of the complex experimental data.
From
the I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry. Academy of Sciences of the U.S.S.R., Leningrad. U.S.S.R. Translation, editing, and publication was supported in part by National Institutes of Health grant HE 07010 to Ernst Simonson. M.D., Mount Sinai Hospital, Minneapolis, Minn. Received for publication Aug. 31. 1970. Reprint requests to: Ernst Simonson. M.D., Mount Sinai Hospital. 2215 Park Ave., Minneapolis, Minn. 55404.
Vol. 83, No. 3, pp. 401-414
March,
1972
American Heart Journal
401
402
Moskalenko
et al.
Features of methods used to study biophysical characteristics of the intracranial circulatory system The following indices were studied in anesthetized animals (dogs, cats, rabbits) : (1) the CSF pressure in the intracranial cavity and vertebral canal, measured by means of tensometric and induction electromanometers1*2 connected to the subarachnoid space in the skull and to the cisterna lumbaris in the spine, and (2) the blood volume in the intracranial cavity, recorded by electroplethysmography,* the biophysical basis of which was described by the writers previously.‘p3 The blood pressures in the carotid artery and in the jugular vein were also recorded, to reflect the conditions of the blood flow into and away from the brain, together with certain other parameters depending on the series of experiments: the systemic venous pressure, electrocardiogram (ECG), respiratory movements, and so on. The techniques used in these experiments are fully described elsewhere.1s3*4 All these parameters were recorded on a 12 channel laboratory instrument, which also was used for the primary processing of the information obtained.5 To study the relationship between the biophysical characteristics of the intracranial circulation, as of any other biophysical system, it is important to choose suitable test procedures which permit the relationships between the parameters under investigation to be changed in determined directions. Small changes in the tested system were analyzed by the use of natural functional variations such as pulse shifts of arterial and venous pressure, which can be regarded as external forces acting on the intracranial circulation. More powerful stresses were applied by the use of orthostatic and occlusive tests, and also of certain clinical tests (Stookey’s and Queckenstedt’s tests). To vary the relationship between volumes and pressures of the fluid media in the closed intracranial cavity, hypervolemia was produced in one
*This
is “Impedance plethysmography.” A more complete list of literature is included in the Introduction of Naumenko and Benua: The physiological mechanisms of cerebral circulation. Springfield, Ill., 1970, Charles C Thomas, Publisher.
Am. Heart J. March, 1972
series of experiments by giving the animals an intravenous injection of polyvinyl (15 ml. per kilogram of body weight). Since the biophysical structure of the intracranial circulation is complex, with numerous connections between its variables, the experimental data were analyzed by methods of mathematical simulation. In this way it was possible to bring together into a single system all the biophysical relationships of the intracranial hemodynamics and to verify its functions. Furthermore, it was also possible to elucidate the functional relationship between those parameters which are difficult to determine experimentally. The model of the intracranial circulatory system was recorded as a program in the ALGOL-60 computer language. For solution of the resulting system of differential equations the numerical method of finite differences6 was used. The approach to the analysis of the experimental data which was adopted determined the order of presentation of the material described in this paper. First an attempt has been made to obtain a basis for the biophysical structure of the intracranial circulation, and then, on the basis of the available factual material, the applicability of this structure has been proved and some aspects examined in regard to some peculiarities of the biophysical characteristics of the intracranial hemodynamics. Biophyrical structure of the intracranial circulatory system From analysis of the considerable volume of experimental material on the intracranial hemodynamics which has now been collected,1~7-10 the structure of the intracranial circulatory system can be represented by the scheme shown in Fig. 1 which, although simplified, nevertheless includes all the principal components. The vascular system of the intracranial cavity is shown in this scheme as a series of spaces, occupied by the arterial (ZNZC) and venous (WVC) systems, with internal pressures of put and PVC, in direct hydraulic contact with the CSF system, and also of intracerebral arteries (~acJ, veins (WVCJ and capillaries (wkc), with internal pressures of Since the PUCi, @Xi, an d pkc, respectively.
Volume Number
83 3
Biophysical
aspects of intracranial
circulation
403
wac,
Fig.
1.
Scheme
of the intracranial
circulatory
system
arterial system of the vertebral canal is poorly developed, and since only a change in volume of the venous plexuses of the spinal cord has any influence on the intracranial hemodynamics,l,” the vascular system of the spinal cord is shown in a simplified form as two spaces filled with venous blood: one of them communicates with the system of the venae cavae below (WVSJ, and the other (VJVS~) above the diaphragm (internal pressures in them, POSZand @&I). The value of this method of subdividing the venous system of the vertebral canal was demonstrated by analysis of the mechanisms of formation of respiratory waves of intracranial pressure.12 The space within the intracranial cavity and vertebral canal occupied by the CSF is represented by a single space, divided into cranial (wlc) and spinal (wls) portions, communicating with each other in the region of the craniovertebral joint through a foramen of limited size. This restricts the velocity of flow of CSF to and fro between the cranial and vertebral cavities, and the time required for stabilization of the intracranial pressure during stepwise changes of intravascular pressure requires as much as 2 to 3 seconds. The vertebral canal possesses definite elasticity, so that it can contain a small additional volume of CSF if displaced, under various conditions, from the intracranial cavity.gJ3J4 The intracranial cavity possesses very little
(symbols
in text).
extensibility : according to the authors’ measurements the elasticity of the intracranial cavity is only a half to a third that of the vertebral canal. The evidence for applicability of the scheme shown in Fig. 1 and the negligible effect of the introduced simplifications has been presented previously.lJ5 This proposed scheme for the simulation of the intracranial circulatory system served as the basis for development of a block diagram of the functional relationships (biophysical structure) of this portion of the vascular system, which is illustrated in Fig. 2. The chief difficulties arising in the construction of the biophysical structure of any physiological system are concerned with the correct choice of direction of the influence of each separate component, allowing for cause-effect relationships and the law of conservation of energy. For this reason the whole complex system of biophysical interconnections of the intracranial circulation is best regarded as a structure consisting of separate subsystems, each of which is characterized by its own conventional “input” and “output” and also by a definite functional link between them. The block diagram of the functional connections in the intracranial hemodynamic system, in which each connection is drawn as a separate structural unit (Fig. 2), to
404
Mosktrlenko
Am. Heart I. March, 1972
et (11.
wm Fig. 2. Block diagramof a modelof the intracranialcirculatory system(symbolsin text).
correspond to the scheme shown in Fig. 1, has the following inputs: (1) blood pressure in arteries conveying blood to the brain Mac>; (2) bl ood pressure in veins carrying blood from the brain (@j); and (3) blood pressure in veins carrying blood from the cranial (@sl) and caudal (@Js~)portions of the spine, i.e., in veins connected with the systems of the inferior and superior venae cavae. The volume of cerebral blood flow (u) depends on the hydraulic resistance of the vascular system of the brain and the pressure drop (API) between the arteries of the base of the skull (pat) and the pial veins (pvc). Any change in the incoming arterial pressure (pat) causes a change in the volume of the arterial system of the brain (wac), which, in turn, changes the CSF pressure in the intracranial cavity (plc). The CSF pressure also depends on the volume of the CSF spaces in the intracranial cavity (wZC), the volume of the venous system of the brain (ZINC), and the volume of the brain tissue (wm). In accordance with existing viewslsll it was accepted that the CSF pressure in the intracranial cavity is in equilibrium with the blood pressure in the pial veins (five), and that the difference (AP2) between this pressure and the pressure in the system of the jugular veins (pvj) determines the velocity of flow of blood from the venous system of the intracranial cavity (q). The
difference between the inflow of blood into the venous system (u) and its outflow (q) determines the increase in volume of venous blood in the intracranial cavity (AWZJC). The blood pressure in the venous plexuses of the spinal cord (pvsl and pvsz) determines the venous volumes in the cranial (ZOVSJand caudal (ZLJVS~) portions of the vertebral canal. The combined volume of the venous system (ZLJZJS~ + wvsz) and the volume of the CSF in the vertebral canal (wls) determine its CSF pressure (pls). The difference between CSF pressures in the intracranial cavity and vertebral canal (API) determines the velocity and direction of the flow of CSF (Awl) between these cavities. The CSF pressure in the intracranial cavity and vertebral canal is also influenced by the elasticity of these cavities. All the functional connections between the various components of the biophysical scheme of the intracranial circulatory system, as listed above, can be subdivided into three groups. The first group of functional relationships relates to volume changes of the vascular system with pressure changes. Such a relationship exists between: (1) the volume and the blood pressure @UC) of the intracranial arterial system (WU) and (2) the volume and the blood pressure (#ws~,pvsz) of the venous plexuses of the spine (WVS~,was,).
Volwne Number
83 3
Biophysical
These relationships are nonlinear,16-1s because of differences in elastic properties of the blood vessel walls, and in accordance with known experimental data” they can be expressed analytically as follows: wi = c + m,(l if Pi > P*,
- ,-capi + b)),
and wi = mz Pi f d if Pi 5 P*
(1)
where : wi represents the volume, Pi the pressure, P* the pressure at which these relationships occur, and a, b, c, d, ml, and mz are constants. The second group of relationships relates to changes of pressure with the volume of fluid in a vessel. Such a relationship exists between: (1) the CSF pressure in the intracranial cavity (plc) and the combined volume of the arterial and venous systems, CSF, and brain tissue in the intracranial cavity (wac + wvc + wlc + wwz); and (2) the CSF pressure in the vertebral canal (pls) and the total volume of the venous system and CSF in this cavity (ZUVS~+ ZLYJS~+ wls). There are no experimental data concerning the character of these relationships. However, using data for the variable elasticity of these two cavities (l), these relationships can be expressed analytically as follows: (hi + 0) Pi = p f m3(e - I>, if wi > w*, and Pi = m,wi + s, if wi 5 w* where:
aspects of intracranial
circulation
405
(2) the velocity of blood flow into the venous system (u) and the pressure difference between the blood in the arteries of the base of the skull and the pial veins (API), and (3) the velocity of blood flow from the venous system (a) and the pressure difference (AP,) between the pial veins and the system of the jugular veins. There are no experimental data on relationships of this type. However, if it is accepted that the venous volume changes only within narrow limits, the velocity of inflow and outflow of blood can be regarded as approximately proportional to the corresponding pressure difference : Vj
= hi X APj
(3)
where : vi represents the velocity of inflow or outflow of blood, APj the pressure difference, and hj is a constant, proportional to the capacity for flow of the corresponding segment of the vascular system. For determination of the velocity of flow of CSF between the cranial and vertebral cavities it is possible, in the authors’ opinion, to use the familiar equations of hydraulics for the case of the flow of fluid through a submerged orifice from one space to another when a pressure difference exists between them.lg In this case the velocity of flow of fluid (AwZ) will be related to the pressure difference of the CSF in the cranial and vertebral cavities (API) by the following equation : Awl = k, X dAP, X API,
(4)
where : (2)
wi represents the volume at which these relationships occur, and f, g, m3, ml, p, and s are constants. The third group of relationships relates to changes of the velocity of flow of fluid between two communicating spaces with a pressure difference. Such a relationship exists between: (1) the velocity of flow of CSF (Awl) and the pressure difference between the CSF in the intracranial cavity and the CSF in the vertebral canal (API),
k, is a coefficient reflecting the configuration of cross section at the place where the cavities are connected. The character of the relationships listed above is demonstrated in the corresponding components of the scheme of the biophysical model of the intracranial circulatory system (Fig. 2). The complex series of biophysical relationships in the intracranial circulatory system can thus be shown by a legible block diagram, with some simplifications (Fig. 1). Should the need arise, individual
406
Moskalenko
Am. Heart J. March, 1972
et al.
components of the biophysical model of the intracranial circulation can be specified in greater detail, thereby bringing them closer to the actual structure. The validity of this biophysical model of the intracranial circulation and its applicability to the analysis of particular states of the intracranial hemodynamics needs experimental verification. The possibility of explaining generally known facts, as well as the results obtained by the authors, relating to fast as well as slow changes in the biophysical parameters of the intracranial hemodynamics through analysis of the proposed biophysical model will be considered next. This analysis will include the possibility of reproduction of these experimental results by application of computer techniques to this model. We define “fast processes” to mean processes which occur only in the intracranial cavity, and as “slow processes” those which evoke compensatory movements of CSF between the intracranial cavity and the vertebral canal. As an approximation, the first group of “fast” processes do not exceed 1 second in duration, while those of the second group (the steady state) are completed within 5 to 6 seconds after the constant force begins to act. To solve this problem it is most convenient to use biophysical parameters such as the intracranial pressure (ICP) and the total blood volume in the intracranial cavity, for on the one hand they are sufficiently simple and accurately recordable under experimental conditions, and on the other, they have the largest number of internal relationships in the system we are considering. Fast changes in the intracranial blood circulation As an example of fast changes in the intracranial hemodynamics it is convenient to examine processes evoked by a natural fluctuation : the cardiac activity. The problems concerned with the effects of the pulse on the basic biophysical parameters of the intracranial circulatory system have been very extensively discussed in recent decades in numerous publications, which can be subdivided into several types of observations. A large series
of articles is concerned with the study of mechanisms of formation of pulse waves of intracranial pressure, although unanimity has not yet been reached on this matter. Some workers, for instance, considered that the leading role in this process is played by arterial pulsation,20 others by venous,21 while a third group is of the opinion that this role belongs to pulsation of both these systems.22 Many articles have been published on the study of pulse fluctuations in the blood volume in the intracranial cavity, using methods of rheoencephalography and intracranial electroplethysmography (impedance plethysmography).23-25 On the clinical plane attempts have been made to find correlations between changes in the parameters of pulse fluctuations in blood volume and the state (particularly pathological states) of the cerebral circulation, while other investigations have attempted to explain the mechanisms of formation of these fluctuations. Whereas the first of these approaches has revealed a number of rigid correlations of diagnostic importance, the second has not yet produced an acceptable explanation of the high variability of amplitude and shape of the pulse waves, and it has done no more than simply state the facts. Finally, there is a special group of investigations concerned with the problem of the presence of pulsation in the closed cavity of the skull, a discussion initiated during Magendie’s time and still continuing today.rv2’j The extent of this indicates the great interest in the examination of pulse change mechanisms in ICP and intracranial blood volume from the standpoint of a biophysical model of the intracranial circulation as illustrated in Fig. 2. If one considers the volumes of the brain and CSF in the intracranial cavity as constant during the pulse cycle, and accepts a linear relationship between the sum of arterial and venous volumes and the ICP (intracavity pressure) for small changes of pressure then it follows from the description given of the intracranial circulatory system that, under whatever conditions it functions, the pulse changes are determined by the equation: 91~ = $ (wac + WC) 1
Y&me Number
83 3
Biophysical
where : ki is a coefficient reflecting the total elasticity of the intracranial cavity. Pulse changes in volume of the arteries of the brain can be regarded, to a satisfactory degree of approximation, as proportional to fluctuations of arterial pressure : wac = kz pat
(6)
where : kz is a coefficient reflecting of the arteries.
the elasticity
With respect to pulse changes in the volume of the venous system in the intracranial cavity it should be noted that, according to Poiseuille’s law, the rate of its change
d(wvc) [ 1 at
depends on the pressure part and the hydraulic veins of the brain (7):
--=d (WC) dt
drop in the venous resistance of the
+ (PZC - pvj).
(7)
Because of the relatively slight changes in volume of the veins in the course of the pulse cycle, the resistance (r) can be taken to be constant. Pulse changes in ICP and blood volume, due in general to changes in arterial and venous pressures, can thus be determined by the simultaneous solution of Equations 5, 6, and 7. If pulsation of the arterial pressure only is present, according to the biophysical model of the intracranial circulatory system (Fig. 2) the pulse waves of ICP will be determined by two processes: pulse changes in volume of the cerebral arteries and fluctuations in the volume of venous blood in the intracranial cavity arising through transmission of the pulse wave from arteries to veins via the CSF, bypassing the capillaries.’ Whereas the first process, according to Equation 6, can be regarded as a linear function of arterial pressure, the relationship between the second process and arterial pressure can be determined by
aspects of intracranial
substituting 7:
circulation
Equations
-- k1Xrd(zmc) ~ ka dt
407
5 and 6 in Equation
-d
(wzx) + T = pat
(8)
where: T is a constant which can be disregarded, as only pulse waves which are characterized by a variable component are being examined. To determine the relationship between periodic changes in venous volume and changes in blood pressure in the arteries of the brain and the conditions under which the volumes of these systems interact, it is convenient to use the amplitude-phase characteristic (APC), which is frequently used in the investigation of complex biological systems. 27,28 In the case under examination, the APC reflects the relationship between venous volume, arterial pressure, and the parameters of the system itself (elasticity of the intracranial cavity kl, elasticity of the walls of the brain arteries k2, hydraulic resistance of the venous system r), and it has the following form:
Ow) L1 (jw) = wzw pat = -\I1 + (r:i2. tan --j x -1 (I. k,.W) .
u)~
1 Examination of the APC (Equation 9) shows that, if the arterial pressure varies periodically with an amplitude of PO and frequency w, changes in the venous volume in the intracranial cavity will be harmonic waves of opposite direction but the same frequency, having an amplitude A0 and shifted in phase through an angle 4: PO X kz Ao = 1 + (r . k1 . o)2 ; C$ = tan-’
(r
k1
w).
(10) It follows from examination of the amplitude characteristic (A,,) that the effect of arterial pulsation on such changes of venous volume in the closed intracranial cavity and, consequently, the degree of divergence between the shapes of the arterial and CSF pulses, will increase with an increase in l
l
408
Moskalenko
et al.
distensibility of the brain arteries (k,), which is equivalent to a decrease in tone of the brain arteries and also to a decrease in elasticity of the cranium (kl), which may be due to an increase in the CSF pressure. The difference between the shapes of the CSF and arterial pulsations will also increase as the pressure rises in the system of the superior vena cava (a decrease in r). A change in heart rate, together with the associated changes in shape of the fluctuations of arterial pressure, will also have an effect on the shape of the CSF pulse, for interaction between the volumes of the arterial and venous systems in the closed intracranial cavity, in accordance with APC-9, is dependent on the spectral composition of the arterial pulsation (w). Whereas an increase in CSF pressure is associated with an increase in amplitude of the changes in venous volume, a decrease in CSF pressure (an increase in k1) causes an increase in the phase shift (4) between the changes in arterial and venous volumes, and this must also be reflected in the shape of the CSF pulsation. The same result is produced by a decrease in the venous pressure and the ensuing increase in hydraulic resistance of the veins (r). Bearing in mind, however, that such changes in parameters are accompanied by a decrease in amplitude of the fluctuations in venous volume, their influence on the ICP is evidently less than when the opposite changes occur in these parameters. In the other extreme case, when pulse waves of ICP are due entirely to venous pulsation, the APC reflecting, as in the case examined above, the relationship between the ICP, the venous pressure, and the ratio between the arterial and venous volumes in the closed intracranial cavity is shown by calculation to be identical in form with APC-9. The effect of a change in the parameters kl, r, and w on the shape of the CSF pulse will be the same as in the case examined above. It should be noted, in particular, that with a change in these parameters the phase shift between the CSF and venous pulses will also be modified. For instance, an increase in blood volume of the venous system in the intracranial cavity (a decrease in r) or an increase in CSF pressure and consequent decrease in kl must reduce the phase shift
Am. Heart J. March, 1972
between the pulse waves of ICP and of the venous pressure. It can thus be concluded from analysis of the structure of the model illustrated in Fig. 2, and from the APC obtained by this analysis, that the formation of pulse waves of ICP and blood volume is a complex process whose ultimate result is determined not only by the characteristics of the forces acting (the arterial and venous pulsations), but also by the conditions of the intracranial hemodynamics as a whole, on which depends the interaction between the volumes of arterial and venous blood and CSF. In other words, it is determined by the biophysical structure of the intracranial circulatory system. These conclusions can be verified by using the APC and by expanding the input values of pat and pvj in a Fourier series, or by using the system of equations obtained and presenting the input signals in numerical form. Since the first method is very laborious, the second was used, and the pulse waves of arterial (pat) and venous ($6) pressures recorded in experiments on animals were fed into the input of the model, and the ICP curves obtained in experiments on animals (pZcl) were compared with those obtained on the model (&). The basic elements of the shape of the curves, their amplitude, and their phase correlation with pulsations of arterial and venous pressure were used as the criterion for this comparison. From the extensive factual material that is available, it is possible to pick out the most typical forms of pulse waves of ICP. At normal levels of arterial and venous pressure the pulse waves of ICP (plcr) shown in Fig. 3 are the most typical. The results of their simulation (plcz) by feeding the pulse waves pat and pvj, recorded in the same animal, into the input of the model are shown in the same figure. It will be apparent from Fig. 3 that the shapes of the pulse waves obtained experimentally and by simulation agree sufficiently closely, and generally repeat the shape of the arterial pulsation. If only the arterial pulsation is fed into the input of the model, the shape of the ICP does not deviate significantly from that shown in Fig. 3. It may thus be concluded that, under experimental conditions close to the animal’s
Volume Number
83 3
Biophysical
aspects of intracranial
circulation
409
10
t,
0
Fig. 3. Results of animal experiment and of simulation under normal conditions of arterial and venous pressure. #UC, Blood pressure in arteries conveying blood to the brain; pvj, blood pressure in veins conveying blood from the brain; @I, CSF pressureanimal experiments; filet, CSF pressure-simulated; t, time axis. This is a qualitative comparison of wave form of $&I and #ZCZ; the amplitude of the simulated tracing pZc, was set to approximate that of pkl, and the units correspond to those in Figs. 4 to 7.
natural state, arterial pulsation plays the leading role in formation of the CSF pulse. However, there is evidence’ to show that exposure even to such mild factors as a change in position of the animal’s body while lowering its head 30 to 40” and also some time thereafter can lead to sharp changes in the shape and amplitude of the pulse waves of ICI’, although the characteristics of arterial pulsation remain unchanged. Consequently, the role of arterial pulsation in formation of the CSF pulse is not always dominant, and the importance of two other factors-venous pulsation (during exposure) and the ratio between the volumes of the fluid media in the closed space (immediately after the stress end)-increases significantly even when the factors concerned are comparatively mild. To create experimental conditions for testing earlier views regarding the possible dominance of the role of venous pulsation in the formation of pulse waves of ICP in animals with a well-marked initial arterial form of their ICP pulse waves, a state of hypervolemia was produced (by the technique described above). This state is characterized by a higher level and increased amplitude of pulsation of the central venous pressure. It is important to note that under these conditions considerable changes take place in the amplitude and shape of the pulse waves of ICP and of
( I at* , e 120 t
IO uo 20
t, Pk.
km HIOJ
120 110
t
136 I.T2
t-
pat hm I$1
Fig. 4. Results of animal experiment and of simulation with intravenous injection of polyvinyl (symbols same as in Fig. 3). This is a qualitative comparison of wave form of @cr and plcr; the amplitude of the simulated tracing pkr was set to approximate that of p1c,.
blood volume,4 indicating essential changes in the intracranial circulatory system. Comparison of the results of simulation (plcz) and experiments (plcr) which were most typical of this particular situation (Fig. 4) shows that considerable--yet parallel-changes in shape and phase shift of intracranial pulsation took place both in the model and in the animal, and that changes in the pulse waves of blood volume were also in the same direction. If arterial pulsation is excluded during simulation of
410
Moskalenko
Am. Heart J. March, 1972
et al.
these experiments, this has no appreciable effect on the shape of CSF pulsation. It cannot yet be concluded, however, that this experimental procedure in fact causes dominance of the venous component in the CSF pulse. The experimental and simulation results described above show that, in general, three principal factors participate in formation of the pulse waves of ICP and blood volume: pulse waves of the arterial volume of the brain, of the venous volume of the brain, and the conditions of the intracranial hemodynamics as a whole. Whereas under near-normal conditions arterial pulsation is characteristically predominant, in circumstances changing the conditions of the intracranial hemodynamics slightly the dominant role moves to venous pulsation. This is presumably the reason for the high variability in shape of the pulse waves of ICP and blood volume under different experimental conditions. The satisfactory agreement between the experimental results and the results obtained by simulation is evidence of the validity of the biophysical model of the intracranial circulatory system illustrated in Fig. 2 for procedures of this nature. Slow processes in the intracranial circulatory system For analysis of slow changes in the biophysical characteristics of the intracranial hemodynamics it is convenient to examine the results of simulation when stepwise changes are made in the values of the input variables. The reaction of any system to such a procedure is highly characteristic, and it is therefore very frequently used for the investigation of complex systems. The authors have used this method to study the intracranial circulatory system, employing both orthostatic and occlusive tests. The dynamics of the intracranial blood volume and intracranial pressure during orthostatic tests were analyzed in detail by the authors previously,’ using a model which was somewhat simplified by comparison with the scheme shown in Fig. 2, and satisfactory agreement was obtained between the calculated and experimental results. The same study also gives extensive experimental data, and equations deter-
WC 1.4 1.0 0.6
Fig. 5. Experimental (I) and simulation (2) curves with compression of jugular veins: a, intracranial pressure; b, blood volume.
mining the relationship between the blood volumes in the intracranial cavity and the ICP during stepwise changes in the intravascular pressure are derived. For that reason, in this paper only the results of simulation, obtained by adapting the scheme shown in Fig. 2 to occlusive tests, will be given in order to make sure that the increased complexity which distinguishes the scheme in Fig. 2 from that examined previously results in a closer resemblance to the actual test object, and not in contradiction of experiments and simulation, These simulation experiments showed that the final steady state of the system is determined entirely by the level of the venous pressure. The CSF pressure in the intracranial cavity becomes stable in about 2 to 3 seconds, but this takes place much more slowly in the vertebral canal. Curves of the dynamics of ICP and blood volume (Fig. 5), obtained by simulation, agree well with the experimental data obtained by occlusion of the jugular veins, which are also presented in this figure. It can also be concluded from examination of Fig. 5 that simulation of the scheme shown in Fig. 2 with the aid of computers gives rather better agreement with the experiments than the analytical examination of the simpler scheme presented by the authors previously,’ i.e., the increase in complexity produces the anticipated better agreement. All these data indicate that
Volume Number
83 3
Biophysical
the biophysical structure of the intracranial circulation examined above corresponds to the real object for the action of slow factors, and, in conjunction with the data on pulse waves, the conclusion may be drawn that this structure is applicable as a whole. Some consequences of analysis biophysical structure of the intracranial circulation
aspects of intracranial
t 1.9
1.7
1.5
411
P!C , /-=-&
t 0
4
6
12
16
20
24
0
4
6
12
16
20
24
of the
Satisfactory agreement between the experimental results and those of simulation of the biophysical structure of the intracranial circulatory system means that the model can be used to make a more detailed examination of the biophysics of the intracranial hemodynamics, which, in some respects, would still be very difficult to carry out experimentally. One of the first problems to be approached is that of the flow of CSF between the intracranial cavity and vertebral canal. The results of simulation show, in this connection, that the flow of CSF between the intracranial cavity and vertebral canal takes place at a constant rate, as is apparent from the curves of blood volumes in the intracranial cavity. This rule governing the CSF flow is evidently explained by the fact of its nonlinear dependence of the pressure difference. Another distinctive feature of the CSF pressure dynamics in the vertebral canal is that the saturation time and shape of the curve are independent of the degree of increase of arterial pressure. The time taken to reach a steady level is likewise independent of the drop in venous pressure, which determines only the magnitude of the final pressure within the vertebral canal. Curves of the dynamics of blood volumes in the intracranial cavity, like those of the CSF pressures in the intracranial cavity and vertebral canal, have three characteristic parts. The first is characterized by a sharp increase in the volume of blood in the intracranial cavity, and its magnitude and duration of increase are determined entirely by the increase in venous pressure; this part of the curve coincides with an increase in ICP. Later, the ICP is maintained at a constant level, but because of the existence of a pressure difference between the intracranial cavity and vertebral
circulation
3.
Kt-
1.0 .-
0
;
6
12
1e
~. 20
24
Fig. 6. Dynamics of (a) intracranial pressure, (b) CSF pressure in vertebral canal, and (c) blood volume in intracranial cavity, for different values of hydraulic resistance to flow of CSF (kg).
canal there is a constant outflow of CSF from the cranium. The second part of the blood volume curve corresponds to this outflow, and the magnitude of the venous pressure drop determines its duration. The results of simulation show that the rate of flow of CSF between the intracranial cavity and vertebral canal has no effect on the final steady state of all the parameters investigated. It also has no effect on the first part of the curves, but its effect on the second part of the curves is considerable because the second part reflects the dynamics of the processes. An increase in the rate of flow, for instance, shortens the time required for stabilization of the ICP (Fig. 6, a) and lowers the level of the second part of the curves. The curves reflecting the dynamics of the CSF pressure in the vertebral canal (Fig. 6, b) show that an increase in the rate of flow of CSF results in the more rapid stabilization of the CSF pressure in the vertebral canal. A similar result is observed in the blood volume curves: the duration
412
1.4
Moskalenko
Am. Heart .I. March. 1972
et al.
t
r 0
4
6
1.2
16
20
24
0
4
2
12
16
26
24
1.4
t,
H..
1.4
1.0
0.6
t
,:,... 0
4
6
12
16
20
24
Fig. 7. Dynamics of (a) intracranial pressure, (b) CSF pressure in vertebral canal, and (c) blood volume in intracranial cavity, for different values of venous resistance (hi).
of the second part is dependent on the rate of flow of CSF. The other parameter of velocity which is an interesting topic for investigation, although difficult to test experimentally, is the rate of the venous outflow. This parameter depends on the hydraulic resistance of the venous system, which is exposed to the influence of the CSF system. Analysis of the simulation results shows that the hydraulic resistance of the venous system has a significant influence on all three parts of the ICP curve (Fig. 7, a), A decrease in the rate of outflow, caused by an increase in the hydraulic resistance, leads to an increase in the ICP level, and also to an increase in the time required to reach the second part. The difference between the stable levels of the second and third parts becomes more apparent as the rate of venous outflow falls. The dynamics of CSF pressure in the vertebral canal in this case (Fig. 7, b) is interesting because the initial part of the curves corresponds to a decrease of pressure, but later, regardless of the velocity
of outflow of blood, the curves are at first identical but then start to diverge. The initial decrease in CSF pressure in the vertebral canal is due to the fact that at the start pls > plc. The steady level of CSF pressure in the vertebral canal, like the ICP, depends on the rate of outflow of the blood. A family of curves reflecting the dynamics of the blood volume is shown in Fig. 7, c. These are interesting because the maximum of the first part, and the time taken to reach it, decrease with an increase in the rate of outflow of the venous blood. The total blood volume in the intracranial cavity also falls. The information concerning the velocities of CSF flow between the intracranial cavity and vertebral canal and of the venous outflow from the cranium obtained by analysis of the model as given above has not yet been confirmed by experimental data, but it points out a concrete way by which experimental proof is possible. By analysis of the model of the biophysical relationships in the intracranial circulatory system it is possible to examine those relationships which determine the influence of the state of this system on the intensity of the cerebral blood flow, which is extremely important both for the understanding of the mechanisms regulating the intracranial circulation under normal conditions and for the study of its disturbances in various pathological states. To solve this problem, certain modifications were introduced into the biophysical model of the intracranial circulatory system (Fig. 2) to enable its elements to be more precisely defined from the quantitative point of view. The vascular system of the brain was examined in accordance with Mchedlishvili’szg classification, represented as six divisions (regional, pial, and intracerebral arteries; capillaries, pial, and main veins) and their quantitative characteristics (mean radius, length, number of vessels) were introduced as for a dog weighing 6 to 8 kilograms. The results obtained by simulation are given in Fig. 8, a. Clearly the intensity of the cerebral blood flow is characterized by complex, nonlinear relationships during changes in the basic biophysical charac-
Volume Number
83 3
Biophysical
aspects of intracranial
be stabilized the arteries,
circulation
413
through a change in lumen of i.e., by active regulation.
Summary
240
160 80 0
Fig. 8. a, Volume velocity of blood flow as a function of arterial pressure and mean radius of resistive vessels; b, character of change in mean radius of resistive vessels during a change in arterial pressure to maintain blood flow at a constant level.
The first conclusion to be drawn from the data on fast and slow processesin the intracranial circulatory system and the results of their simulation described in this paper is that a sufficiently comprehensive group of data is now available for defining the biophysical structure of the intracranial circulatory system and for representing it by a functioning model, the investigation of which yields results that are in satisfactory agreement with the experimental data. As a result of investigation of such a model, as has been shown above, it is possible not only to clarify existing concepts of the mechanisms determining the dynamics of the principal biophysical characteristics of the intracranial circulatory system, but also to discover relationships not previously demonstrable by experimental methods. It is very important to note that analysis of the biophysical structure of the intracranial circulatory system also indicates those components which have been inadequately studied, thus setting the trend for future research. REFERENCES 1.
teristics of the intracranial circulatory system. Investigations of this model show, in particular, how the lumen of resistive vessels must change in order to stabilize the cerebral blood Aow when changes of arterial pressure occur (Fig. 8, b). It is very important to note that, as a result of simulation, the existence of unstable zones in the intracranial circulatory system has been discovered, both at certain values of the arterial, venous, and CSF pressures and also for certain values of the radius of the intracerebral arteries. Are these zones of instability the cause of acute disturbances of the cerebral blood flow in certain pathological states? It is difficult at present to say whether this is true or not, but at least it provides a concrete basis for further research in this direction. The characteristics obtained indicate that definite limits to changes in the biophysical parameters of the system exist, within which the cerebral blood flow can
2.
3.
4.
5.
6.
Moskalenko, Yu. E.: Dynamics of the blood volume of the brain under normal conditions and during gravitational loads, Leningrad, 1967, Nauka (Russ.). Moskalenko, Yu. E.: Telemetrical equipment for studying blood circulation of the brain, J. Physiol. 172:3, 1964. Moskalenko, Yu. E., and Naumenko, A.: Hemodynamics of cerebral circulation, in Cerebral ischemia, Springfield, Ill., 1964, Charles C Thomas, Publisher, p. 21. Dansker, V. L., Moskalenko, Yu. E., Sorokoumov, V. A., and Vainshtein, G. B.: Measurement of intracranial pressure and its pulse and respiratory fluctuations after intravenous injection of hypertonic solution, Fiziol. Zh. S.S.S.R. 54:1295, 1968 (Russ.). Demchenko, I. T.: Method of studying the local blood supply to the brain, Fiziol. Zh. S.S.S.R. 54:1123, 1968 (Russ.). Bellman, R., and Cooke, K. L.: Differentialdifference equations, New York and London, 1963, Academic Press. Mosso, A.: iiber Kreislauf des Blutes im menschlichen Gehirn. Leiozip. 1881. Veit & Coma. Geigel, R.: Die Rolle des Liquor cerebrospinaiis bei der Circulation im Schzdel, Pflueger. Arch. 109:337, 1905. Becher, E.: Untersuchungen iiber die Dynamik ,
IO,
,
414
IO.
11.
12. 13. 14.
15.
16. 17.
18. 19.
Moskalenko
et (11.
des Liquor cerebrospinalis, Mitt. Grenzgeb. Med. Chir. 35:366, 1922. Kedrov, A. A., and Naumenko, A. I.: Problems in physiology of the intracranial circulation with their clinical interpretation, Leningrad, 19.54, Medgiz (Russ.). Vasilevskii, N. N., and Naumenko, A. I.: Velocity of the cerebral blood flow and movement of the cerebrosoinal fluid, Leningrad, 1959, Medgiz (Russ.). * Vainshtein, G. B.: Origin of the respiratory waves of intracranial pressure, Fiziol. Zh. S.S.S.R. 55:1253, 1969 (Russ.). Flexner, L. B., Clark, J. H., and Weed, L. H.: The elasticity of the dural sac and its contents, Amer. J. Physiol. 102:292, 1932. Moskalenko, Yu. E., and Naumenko, A. I.: Investigation of the character of CSF movement in normal animals, Fiziol. Zh. S.S.S.R. 45:562, 1959 (Russ.). Kislyakov, Yu. Ya. : Mathematical simulation of intracranial hemodynamics by the method of finite differences, Biofizika 14:179, 1969 (Russ.). Bergel, D. H.: The static elastic properties of the arterial wall. I. Phvsiol. 156:445, 1961. Savitskii, N. N.1 Biopdysicai basis of the circulation of the blood and clinical methods of study of the hemodynamics, Leningrad, 1963, Publisher Medgiz (Russ.). Rashevsky, N.ySome medical aspects of mathematical biology, Springfield, Ill., 1964, Charles C Thomas, Publisher. Kiselev, P. G.: Hydraulics, Leningrad, 1963, Publisher Gosenergoisdat (Russ.).
Am. Heart J. March, 1972
20. Bering, E. A.: Choroid plexus and arterial pulsation of cerebrospinal fluid, Arch. Neurol. Psychiat. 73:165, 1955. 21. Hamit, H. F., Beall, A. C., and De Bakey, M. E.: Hemodynamic influences upon brain and CSF; pulsations and pressures, J. Trauma 5:174, 1965. 22. Adolph, R. J., Fukusumi, H., and Fower, N. 0.: Origin of cerebrospinal fluid pulsations, Amer. J. Physiol. 212:840, 1967. 23. Jenkner, F. L.: Rheo-encephalography, Springfield, Ill., 1962, Charles C Thomas, Publisher. 24. Namon, R., Gallan, F., Schimojo, S., Sano, R. M., Markovich, S. E., and Scheinberg, P.: Basic study in rheoencephalography, Neurology 17:239, 1967. 25. Yarulin, Kh. Kh.: Diagnosis of pathological tortuosity of the carotid arteries by rheoencephalography, Zh. Nevropat. Psikhiat. 65: 1476, 1965 (Russ.). 26. Klosovskii, V. N.: Circulation of blood in the brain, Moscow, 1951 (Russ.). Translation: Office of Technical Service, Washington, 1963, U. S. Dept. of Commerce. 27. Grodins, F. S.: Control theory and biological systems, New York, 1963, Columbia University Press. 28. Milsum, J. H.: Biological control system analysis, New York, 1966, McGraw-Hill Book Co., Inc. 29. Mchedlishvili, G. I.: Functions of the vascular mechanisms of the brain, Leningrad, 1968, Naukoi, publisher. (Russ.).
Biophysical
aspects
of the intracranial
circulation
Yu. E. Moskalenko Yu. Ya. Kislyakov G. B. Vainshtein B. B. Zelikson Leningrad, U.S.S.R.
T
he biophysical structure of intracranial hemodynamics is determined primarily by the structural features distinguishing the vascular system of the brain and of the cerebrospinal cavity as a whole. Foremost among these is the limitation of the capacity of the cranial cavity, which is responsible for the complex character of the relationships between volumes and pressures of the fluid media-arterial and venous blood, cerebrospinal fluid (CSF)-inside the closed skull. The relationships between volumes and pressures of the blood in the cranial and vertebral cavities, effected through the flow of CSF to and fro between them, are another important consideration. With existing techniques, it is possible to record the cerebral blood flow accurately only by means of the Kety-Schmidt method, with its high inertia, or by variations of this method. The basic biophysical parameters of the intracranial hemodynamics (intracranial blood volume, intracranial pressure) are recorded by relatively simple and exceedingly dynamic
methods.’ Data concerning changes in these parameters also are interesting because, unlike data for the volume of the cerebral blood flow, they can indicate rapid changes in the intracranial circulatory system blood flow, and provide some information about the “stress” placed on the control system of the intracranial circulation and of its powers of compensation. However, the absence of any unanimously accepted concept of the biophysical structure of the intracranial circulatory system has led, at the present time, to the accumulation of many facts that are difficult to explain-facts which complicate still further the already confused notions concerning the function of this important physiological system. Therefore, we will attempt in this paper to organize the accumulated data of our investigations on the biophysics of the intracranial circulation. We will propose a hypothesis of the biophysical structure of cerebral circulation, which will contribute to the understanding of the complex experimental data.
From
the I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry. Academy of Sciences of the U.S.S.R., Leningrad. U.S.S.R. Translation, editing, and publication was supported in part by National Institutes of Health grant HE 07010 to Ernst Simonson. M.D., Mount Sinai Hospital, Minneapolis, Minn. Received for publication Aug. 31. 1970. Reprint requests to: Ernst Simonson. M.D., Mount Sinai Hospital. 2215 Park Ave., Minneapolis, Minn. 55404.
Vol. 83, No. 3, pp. 401-414
March,
1972
American Heart Journal
401
402
Moskalenko
et al.
Features of methods used to study biophysical characteristics of the intracranial circulatory system The following indices were studied in anesthetized animals (dogs, cats, rabbits) : (1) the CSF pressure in the intracranial cavity and vertebral canal, measured by means of tensometric and induction electromanometers1*2 connected to the subarachnoid space in the skull and to the cisterna lumbaris in the spine, and (2) the blood volume in the intracranial cavity, recorded by electroplethysmography,* the biophysical basis of which was described by the writers previously.‘p3 The blood pressures in the carotid artery and in the jugular vein were also recorded, to reflect the conditions of the blood flow into and away from the brain, together with certain other parameters depending on the series of experiments: the systemic venous pressure, electrocardiogram (ECG), respiratory movements, and so on. The techniques used in these experiments are fully described elsewhere.1s3*4 All these parameters were recorded on a 12 channel laboratory instrument, which also was used for the primary processing of the information obtained.5 To study the relationship between the biophysical characteristics of the intracranial circulation, as of any other biophysical system, it is important to choose suitable test procedures which permit the relationships between the parameters under investigation to be changed in determined directions. Small changes in the tested system were analyzed by the use of natural functional variations such as pulse shifts of arterial and venous pressure, which can be regarded as external forces acting on the intracranial circulation. More powerful stresses were applied by the use of orthostatic and occlusive tests, and also of certain clinical tests (Stookey’s and Queckenstedt’s tests). To vary the relationship between volumes and pressures of the fluid media in the closed intracranial cavity, hypervolemia was produced in one
*This
is “Impedance plethysmography.” A more complete list of literature is included in the Introduction of Naumenko and Benua: The physiological mechanisms of cerebral circulation. Springfield, Ill., 1970, Charles C Thomas, Publisher.
Am. Heart J. March, 1972
series of experiments by giving the animals an intravenous injection of polyvinyl (15 ml. per kilogram of body weight). Since the biophysical structure of the intracranial circulation is complex, with numerous connections between its variables, the experimental data were analyzed by methods of mathematical simulation. In this way it was possible to bring together into a single system all the biophysical relationships of the intracranial hemodynamics and to verify its functions. Furthermore, it was also possible to elucidate the functional relationship between those parameters which are difficult to determine experimentally. The model of the intracranial circulatory system was recorded as a program in the ALGOL-60 computer language. For solution of the resulting system of differential equations the numerical method of finite differences6 was used. The approach to the analysis of the experimental data which was adopted determined the order of presentation of the material described in this paper. First an attempt has been made to obtain a basis for the biophysical structure of the intracranial circulation, and then, on the basis of the available factual material, the applicability of this structure has been proved and some aspects examined in regard to some peculiarities of the biophysical characteristics of the intracranial hemodynamics. Biophyrical structure of the intracranial circulatory system From analysis of the considerable volume of experimental material on the intracranial hemodynamics which has now been collected,1~7-10 the structure of the intracranial circulatory system can be represented by the scheme shown in Fig. 1 which, although simplified, nevertheless includes all the principal components. The vascular system of the intracranial cavity is shown in this scheme as a series of spaces, occupied by the arterial (ZNZC) and venous (WVC) systems, with internal pressures of put and PVC, in direct hydraulic contact with the CSF system, and also of intracerebral arteries (~acJ, veins (WVCJ and capillaries (wkc), with internal pressures of Since the PUCi, @Xi, an d pkc, respectively.
Volume Number
83 3
Biophysical
aspects of intracranial
circulation
403
wac,
Fig.
1.
Scheme
of the intracranial
circulatory
system
arterial system of the vertebral canal is poorly developed, and since only a change in volume of the venous plexuses of the spinal cord has any influence on the intracranial hemodynamics,l,” the vascular system of the spinal cord is shown in a simplified form as two spaces filled with venous blood: one of them communicates with the system of the venae cavae below (WVSJ, and the other (VJVS~) above the diaphragm (internal pressures in them, POSZand @&I). The value of this method of subdividing the venous system of the vertebral canal was demonstrated by analysis of the mechanisms of formation of respiratory waves of intracranial pressure.12 The space within the intracranial cavity and vertebral canal occupied by the CSF is represented by a single space, divided into cranial (wlc) and spinal (wls) portions, communicating with each other in the region of the craniovertebral joint through a foramen of limited size. This restricts the velocity of flow of CSF to and fro between the cranial and vertebral cavities, and the time required for stabilization of the intracranial pressure during stepwise changes of intravascular pressure requires as much as 2 to 3 seconds. The vertebral canal possesses definite elasticity, so that it can contain a small additional volume of CSF if displaced, under various conditions, from the intracranial cavity.gJ3J4 The intracranial cavity possesses very little
(symbols
in text).
extensibility : according to the authors’ measurements the elasticity of the intracranial cavity is only a half to a third that of the vertebral canal. The evidence for applicability of the scheme shown in Fig. 1 and the negligible effect of the introduced simplifications has been presented previously.lJ5 This proposed scheme for the simulation of the intracranial circulatory system served as the basis for development of a block diagram of the functional relationships (biophysical structure) of this portion of the vascular system, which is illustrated in Fig. 2. The chief difficulties arising in the construction of the biophysical structure of any physiological system are concerned with the correct choice of direction of the influence of each separate component, allowing for cause-effect relationships and the law of conservation of energy. For this reason the whole complex system of biophysical interconnections of the intracranial circulation is best regarded as a structure consisting of separate subsystems, each of which is characterized by its own conventional “input” and “output” and also by a definite functional link between them. The block diagram of the functional connections in the intracranial hemodynamic system, in which each connection is drawn as a separate structural unit (Fig. 2), to
404
Mosktrlenko
Am. Heart I. March, 1972
et (11.
wm Fig. 2. Block diagramof a modelof the intracranialcirculatory system(symbolsin text).
correspond to the scheme shown in Fig. 1, has the following inputs: (1) blood pressure in arteries conveying blood to the brain Mac>; (2) bl ood pressure in veins carrying blood from the brain (@j); and (3) blood pressure in veins carrying blood from the cranial (@sl) and caudal (@Js~)portions of the spine, i.e., in veins connected with the systems of the inferior and superior venae cavae. The volume of cerebral blood flow (u) depends on the hydraulic resistance of the vascular system of the brain and the pressure drop (API) between the arteries of the base of the skull (pat) and the pial veins (pvc). Any change in the incoming arterial pressure (pat) causes a change in the volume of the arterial system of the brain (wac), which, in turn, changes the CSF pressure in the intracranial cavity (plc). The CSF pressure also depends on the volume of the CSF spaces in the intracranial cavity (wZC), the volume of the venous system of the brain (ZINC), and the volume of the brain tissue (wm). In accordance with existing viewslsll it was accepted that the CSF pressure in the intracranial cavity is in equilibrium with the blood pressure in the pial veins (five), and that the difference (AP2) between this pressure and the pressure in the system of the jugular veins (pvj) determines the velocity of flow of blood from the venous system of the intracranial cavity (q). The
difference between the inflow of blood into the venous system (u) and its outflow (q) determines the increase in volume of venous blood in the intracranial cavity (AWZJC). The blood pressure in the venous plexuses of the spinal cord (pvsl and pvsz) determines the venous volumes in the cranial (ZOVSJand caudal (ZLJVS~) portions of the vertebral canal. The combined volume of the venous system (ZLJZJS~ + wvsz) and the volume of the CSF in the vertebral canal (wls) determine its CSF pressure (pls). The difference between CSF pressures in the intracranial cavity and vertebral canal (API) determines the velocity and direction of the flow of CSF (Awl) between these cavities. The CSF pressure in the intracranial cavity and vertebral canal is also influenced by the elasticity of these cavities. All the functional connections between the various components of the biophysical scheme of the intracranial circulatory system, as listed above, can be subdivided into three groups. The first group of functional relationships relates to volume changes of the vascular system with pressure changes. Such a relationship exists between: (1) the volume and the blood pressure @UC) of the intracranial arterial system (WU) and (2) the volume and the blood pressure (#ws~,pvsz) of the venous plexuses of the spine (WVS~,was,).
Volwne Number
83 3
Biophysical
These relationships are nonlinear,16-1s because of differences in elastic properties of the blood vessel walls, and in accordance with known experimental data” they can be expressed analytically as follows: wi = c + m,(l if Pi > P*,
- ,-capi + b)),
and wi = mz Pi f d if Pi 5 P*
(1)
where : wi represents the volume, Pi the pressure, P* the pressure at which these relationships occur, and a, b, c, d, ml, and mz are constants. The second group of relationships relates to changes of pressure with the volume of fluid in a vessel. Such a relationship exists between: (1) the CSF pressure in the intracranial cavity (plc) and the combined volume of the arterial and venous systems, CSF, and brain tissue in the intracranial cavity (wac + wvc + wlc + wwz); and (2) the CSF pressure in the vertebral canal (pls) and the total volume of the venous system and CSF in this cavity (ZUVS~+ ZLYJS~+ wls). There are no experimental data concerning the character of these relationships. However, using data for the variable elasticity of these two cavities (l), these relationships can be expressed analytically as follows: (hi + 0) Pi = p f m3(e - I>, if wi > w*, and Pi = m,wi + s, if wi 5 w* where:
aspects of intracranial
circulation
405
(2) the velocity of blood flow into the venous system (u) and the pressure difference between the blood in the arteries of the base of the skull and the pial veins (API), and (3) the velocity of blood flow from the venous system (a) and the pressure difference (AP,) between the pial veins and the system of the jugular veins. There are no experimental data on relationships of this type. However, if it is accepted that the venous volume changes only within narrow limits, the velocity of inflow and outflow of blood can be regarded as approximately proportional to the corresponding pressure difference : Vj
= hi X APj
(3)
where : vi represents the velocity of inflow or outflow of blood, APj the pressure difference, and hj is a constant, proportional to the capacity for flow of the corresponding segment of the vascular system. For determination of the velocity of flow of CSF between the cranial and vertebral cavities it is possible, in the authors’ opinion, to use the familiar equations of hydraulics for the case of the flow of fluid through a submerged orifice from one space to another when a pressure difference exists between them.lg In this case the velocity of flow of fluid (AwZ) will be related to the pressure difference of the CSF in the cranial and vertebral cavities (API) by the following equation : Awl = k, X dAP, X API,
(4)
where : (2)
wi represents the volume at which these relationships occur, and f, g, m3, ml, p, and s are constants. The third group of relationships relates to changes of the velocity of flow of fluid between two communicating spaces with a pressure difference. Such a relationship exists between: (1) the velocity of flow of CSF (Awl) and the pressure difference between the CSF in the intracranial cavity and the CSF in the vertebral canal (API),
k, is a coefficient reflecting the configuration of cross section at the place where the cavities are connected. The character of the relationships listed above is demonstrated in the corresponding components of the scheme of the biophysical model of the intracranial circulatory system (Fig. 2). The complex series of biophysical relationships in the intracranial circulatory system can thus be shown by a legible block diagram, with some simplifications (Fig. 1). Should the need arise, individual
406
Moskalenko
Am. Heart J. March, 1972
et al.
components of the biophysical model of the intracranial circulation can be specified in greater detail, thereby bringing them closer to the actual structure. The validity of this biophysical model of the intracranial circulation and its applicability to the analysis of particular states of the intracranial hemodynamics needs experimental verification. The possibility of explaining generally known facts, as well as the results obtained by the authors, relating to fast as well as slow changes in the biophysical parameters of the intracranial hemodynamics through analysis of the proposed biophysical model will be considered next. This analysis will include the possibility of reproduction of these experimental results by application of computer techniques to this model. We define “fast processes” to mean processes which occur only in the intracranial cavity, and as “slow processes” those which evoke compensatory movements of CSF between the intracranial cavity and the vertebral canal. As an approximation, the first group of “fast” processes do not exceed 1 second in duration, while those of the second group (the steady state) are completed within 5 to 6 seconds after the constant force begins to act. To solve this problem it is most convenient to use biophysical parameters such as the intracranial pressure (ICP) and the total blood volume in the intracranial cavity, for on the one hand they are sufficiently simple and accurately recordable under experimental conditions, and on the other, they have the largest number of internal relationships in the system we are considering. Fast changes in the intracranial blood circulation As an example of fast changes in the intracranial hemodynamics it is convenient to examine processes evoked by a natural fluctuation : the cardiac activity. The problems concerned with the effects of the pulse on the basic biophysical parameters of the intracranial circulatory system have been very extensively discussed in recent decades in numerous publications, which can be subdivided into several types of observations. A large series
of articles is concerned with the study of mechanisms of formation of pulse waves of intracranial pressure, although unanimity has not yet been reached on this matter. Some workers, for instance, considered that the leading role in this process is played by arterial pulsation,20 others by venous,21 while a third group is of the opinion that this role belongs to pulsation of both these systems.22 Many articles have been published on the study of pulse fluctuations in the blood volume in the intracranial cavity, using methods of rheoencephalography and intracranial electroplethysmography (impedance plethysmography).23-25 On the clinical plane attempts have been made to find correlations between changes in the parameters of pulse fluctuations in blood volume and the state (particularly pathological states) of the cerebral circulation, while other investigations have attempted to explain the mechanisms of formation of these fluctuations. Whereas the first of these approaches has revealed a number of rigid correlations of diagnostic importance, the second has not yet produced an acceptable explanation of the high variability of amplitude and shape of the pulse waves, and it has done no more than simply state the facts. Finally, there is a special group of investigations concerned with the problem of the presence of pulsation in the closed cavity of the skull, a discussion initiated during Magendie’s time and still continuing today.rv2’j The extent of this indicates the great interest in the examination of pulse change mechanisms in ICP and intracranial blood volume from the standpoint of a biophysical model of the intracranial circulation as illustrated in Fig. 2. If one considers the volumes of the brain and CSF in the intracranial cavity as constant during the pulse cycle, and accepts a linear relationship between the sum of arterial and venous volumes and the ICP (intracavity pressure) for small changes of pressure then it follows from the description given of the intracranial circulatory system that, under whatever conditions it functions, the pulse changes are determined by the equation: 91~ = $ (wac + WC) 1
Y&me Number
83 3
Biophysical
where : ki is a coefficient reflecting the total elasticity of the intracranial cavity. Pulse changes in volume of the arteries of the brain can be regarded, to a satisfactory degree of approximation, as proportional to fluctuations of arterial pressure : wac = kz pat
(6)
where : kz is a coefficient reflecting of the arteries.
the elasticity
With respect to pulse changes in the volume of the venous system in the intracranial cavity it should be noted that, according to Poiseuille’s law, the rate of its change
d(wvc) [ 1 at
depends on the pressure part and the hydraulic veins of the brain (7):
--=d (WC) dt
drop in the venous resistance of the
+ (PZC - pvj).
(7)
Because of the relatively slight changes in volume of the veins in the course of the pulse cycle, the resistance (r) can be taken to be constant. Pulse changes in ICP and blood volume, due in general to changes in arterial and venous pressures, can thus be determined by the simultaneous solution of Equations 5, 6, and 7. If pulsation of the arterial pressure only is present, according to the biophysical model of the intracranial circulatory system (Fig. 2) the pulse waves of ICP will be determined by two processes: pulse changes in volume of the cerebral arteries and fluctuations in the volume of venous blood in the intracranial cavity arising through transmission of the pulse wave from arteries to veins via the CSF, bypassing the capillaries.’ Whereas the first process, according to Equation 6, can be regarded as a linear function of arterial pressure, the relationship between the second process and arterial pressure can be determined by
aspects of intracranial
substituting 7:
circulation
Equations
-- k1Xrd(zmc) ~ ka dt
407
5 and 6 in Equation
-d
(wzx) + T = pat
(8)
where: T is a constant which can be disregarded, as only pulse waves which are characterized by a variable component are being examined. To determine the relationship between periodic changes in venous volume and changes in blood pressure in the arteries of the brain and the conditions under which the volumes of these systems interact, it is convenient to use the amplitude-phase characteristic (APC), which is frequently used in the investigation of complex biological systems. 27,28 In the case under examination, the APC reflects the relationship between venous volume, arterial pressure, and the parameters of the system itself (elasticity of the intracranial cavity kl, elasticity of the walls of the brain arteries k2, hydraulic resistance of the venous system r), and it has the following form:
Ow) L1 (jw) = wzw pat = -\I1 + (r:i2. tan --j x -1 (I. k,.W) .
u)~
1 Examination of the APC (Equation 9) shows that, if the arterial pressure varies periodically with an amplitude of PO and frequency w, changes in the venous volume in the intracranial cavity will be harmonic waves of opposite direction but the same frequency, having an amplitude A0 and shifted in phase through an angle 4: PO X kz Ao = 1 + (r . k1 . o)2 ; C$ = tan-’
(r
k1
w).
(10) It follows from examination of the amplitude characteristic (A,,) that the effect of arterial pulsation on such changes of venous volume in the closed intracranial cavity and, consequently, the degree of divergence between the shapes of the arterial and CSF pulses, will increase with an increase in l
l
408
Moskalenko
et al.
distensibility of the brain arteries (k,), which is equivalent to a decrease in tone of the brain arteries and also to a decrease in elasticity of the cranium (kl), which may be due to an increase in the CSF pressure. The difference between the shapes of the CSF and arterial pulsations will also increase as the pressure rises in the system of the superior vena cava (a decrease in r). A change in heart rate, together with the associated changes in shape of the fluctuations of arterial pressure, will also have an effect on the shape of the CSF pulse, for interaction between the volumes of the arterial and venous systems in the closed intracranial cavity, in accordance with APC-9, is dependent on the spectral composition of the arterial pulsation (w). Whereas an increase in CSF pressure is associated with an increase in amplitude of the changes in venous volume, a decrease in CSF pressure (an increase in k1) causes an increase in the phase shift (4) between the changes in arterial and venous volumes, and this must also be reflected in the shape of the CSF pulsation. The same result is produced by a decrease in the venous pressure and the ensuing increase in hydraulic resistance of the veins (r). Bearing in mind, however, that such changes in parameters are accompanied by a decrease in amplitude of the fluctuations in venous volume, their influence on the ICP is evidently less than when the opposite changes occur in these parameters. In the other extreme case, when pulse waves of ICP are due entirely to venous pulsation, the APC reflecting, as in the case examined above, the relationship between the ICP, the venous pressure, and the ratio between the arterial and venous volumes in the closed intracranial cavity is shown by calculation to be identical in form with APC-9. The effect of a change in the parameters kl, r, and w on the shape of the CSF pulse will be the same as in the case examined above. It should be noted, in particular, that with a change in these parameters the phase shift between the CSF and venous pulses will also be modified. For instance, an increase in blood volume of the venous system in the intracranial cavity (a decrease in r) or an increase in CSF pressure and consequent decrease in kl must reduce the phase shift
Am. Heart J. March, 1972
between the pulse waves of ICP and of the venous pressure. It can thus be concluded from analysis of the structure of the model illustrated in Fig. 2, and from the APC obtained by this analysis, that the formation of pulse waves of ICP and blood volume is a complex process whose ultimate result is determined not only by the characteristics of the forces acting (the arterial and venous pulsations), but also by the conditions of the intracranial hemodynamics as a whole, on which depends the interaction between the volumes of arterial and venous blood and CSF. In other words, it is determined by the biophysical structure of the intracranial circulatory system. These conclusions can be verified by using the APC and by expanding the input values of pat and pvj in a Fourier series, or by using the system of equations obtained and presenting the input signals in numerical form. Since the first method is very laborious, the second was used, and the pulse waves of arterial (pat) and venous ($6) pressures recorded in experiments on animals were fed into the input of the model, and the ICP curves obtained in experiments on animals (pZcl) were compared with those obtained on the model (&). The basic elements of the shape of the curves, their amplitude, and their phase correlation with pulsations of arterial and venous pressure were used as the criterion for this comparison. From the extensive factual material that is available, it is possible to pick out the most typical forms of pulse waves of ICP. At normal levels of arterial and venous pressure the pulse waves of ICP (plcr) shown in Fig. 3 are the most typical. The results of their simulation (plcz) by feeding the pulse waves pat and pvj, recorded in the same animal, into the input of the model are shown in the same figure. It will be apparent from Fig. 3 that the shapes of the pulse waves obtained experimentally and by simulation agree sufficiently closely, and generally repeat the shape of the arterial pulsation. If only the arterial pulsation is fed into the input of the model, the shape of the ICP does not deviate significantly from that shown in Fig. 3. It may thus be concluded that, under experimental conditions close to the animal’s
Volume Number
83 3
Biophysical
aspects of intracranial
circulation
409
10
t,
0
Fig. 3. Results of animal experiment and of simulation under normal conditions of arterial and venous pressure. #UC, Blood pressure in arteries conveying blood to the brain; pvj, blood pressure in veins conveying blood from the brain; @I, CSF pressureanimal experiments; filet, CSF pressure-simulated; t, time axis. This is a qualitative comparison of wave form of $&I and #ZCZ; the amplitude of the simulated tracing pZc, was set to approximate that of pkl, and the units correspond to those in Figs. 4 to 7.
natural state, arterial pulsation plays the leading role in formation of the CSF pulse. However, there is evidence’ to show that exposure even to such mild factors as a change in position of the animal’s body while lowering its head 30 to 40” and also some time thereafter can lead to sharp changes in the shape and amplitude of the pulse waves of ICI’, although the characteristics of arterial pulsation remain unchanged. Consequently, the role of arterial pulsation in formation of the CSF pulse is not always dominant, and the importance of two other factors-venous pulsation (during exposure) and the ratio between the volumes of the fluid media in the closed space (immediately after the stress end)-increases significantly even when the factors concerned are comparatively mild. To create experimental conditions for testing earlier views regarding the possible dominance of the role of venous pulsation in the formation of pulse waves of ICP in animals with a well-marked initial arterial form of their ICP pulse waves, a state of hypervolemia was produced (by the technique described above). This state is characterized by a higher level and increased amplitude of pulsation of the central venous pressure. It is important to note that under these conditions considerable changes take place in the amplitude and shape of the pulse waves of ICP and of
( I at* , e 120 t
IO uo 20
t, Pk.
km HIOJ
120 110
t
136 I.T2
t-
pat hm I$1
Fig. 4. Results of animal experiment and of simulation with intravenous injection of polyvinyl (symbols same as in Fig. 3). This is a qualitative comparison of wave form of @cr and plcr; the amplitude of the simulated tracing pkr was set to approximate that of p1c,.
blood volume,4 indicating essential changes in the intracranial circulatory system. Comparison of the results of simulation (plcz) and experiments (plcr) which were most typical of this particular situation (Fig. 4) shows that considerable--yet parallel-changes in shape and phase shift of intracranial pulsation took place both in the model and in the animal, and that changes in the pulse waves of blood volume were also in the same direction. If arterial pulsation is excluded during simulation of
410
Moskalenko
Am. Heart J. March, 1972
et al.
these experiments, this has no appreciable effect on the shape of CSF pulsation. It cannot yet be concluded, however, that this experimental procedure in fact causes dominance of the venous component in the CSF pulse. The experimental and simulation results described above show that, in general, three principal factors participate in formation of the pulse waves of ICP and blood volume: pulse waves of the arterial volume of the brain, of the venous volume of the brain, and the conditions of the intracranial hemodynamics as a whole. Whereas under near-normal conditions arterial pulsation is characteristically predominant, in circumstances changing the conditions of the intracranial hemodynamics slightly the dominant role moves to venous pulsation. This is presumably the reason for the high variability in shape of the pulse waves of ICP and blood volume under different experimental conditions. The satisfactory agreement between the experimental results and the results obtained by simulation is evidence of the validity of the biophysical model of the intracranial circulatory system illustrated in Fig. 2 for procedures of this nature. Slow processes in the intracranial circulatory system For analysis of slow changes in the biophysical characteristics of the intracranial hemodynamics it is convenient to examine the results of simulation when stepwise changes are made in the values of the input variables. The reaction of any system to such a procedure is highly characteristic, and it is therefore very frequently used for the investigation of complex systems. The authors have used this method to study the intracranial circulatory system, employing both orthostatic and occlusive tests. The dynamics of the intracranial blood volume and intracranial pressure during orthostatic tests were analyzed in detail by the authors previously,’ using a model which was somewhat simplified by comparison with the scheme shown in Fig. 2, and satisfactory agreement was obtained between the calculated and experimental results. The same study also gives extensive experimental data, and equations deter-
WC 1.4 1.0 0.6
Fig. 5. Experimental (I) and simulation (2) curves with compression of jugular veins: a, intracranial pressure; b, blood volume.
mining the relationship between the blood volumes in the intracranial cavity and the ICP during stepwise changes in the intravascular pressure are derived. For that reason, in this paper only the results of simulation, obtained by adapting the scheme shown in Fig. 2 to occlusive tests, will be given in order to make sure that the increased complexity which distinguishes the scheme in Fig. 2 from that examined previously results in a closer resemblance to the actual test object, and not in contradiction of experiments and simulation, These simulation experiments showed that the final steady state of the system is determined entirely by the level of the venous pressure. The CSF pressure in the intracranial cavity becomes stable in about 2 to 3 seconds, but this takes place much more slowly in the vertebral canal. Curves of the dynamics of ICP and blood volume (Fig. 5), obtained by simulation, agree well with the experimental data obtained by occlusion of the jugular veins, which are also presented in this figure. It can also be concluded from examination of Fig. 5 that simulation of the scheme shown in Fig. 2 with the aid of computers gives rather better agreement with the experiments than the analytical examination of the simpler scheme presented by the authors previously,’ i.e., the increase in complexity produces the anticipated better agreement. All these data indicate that
Volume Number
83 3
Biophysical
the biophysical structure of the intracranial circulation examined above corresponds to the real object for the action of slow factors, and, in conjunction with the data on pulse waves, the conclusion may be drawn that this structure is applicable as a whole. Some consequences of analysis biophysical structure of the intracranial circulation
aspects of intracranial
t 1.9
1.7
1.5
411
P!C , /-=-&
t 0
4
6
12
16
20
24
0
4
6
12
16
20
24
of the
Satisfactory agreement between the experimental results and those of simulation of the biophysical structure of the intracranial circulatory system means that the model can be used to make a more detailed examination of the biophysics of the intracranial hemodynamics, which, in some respects, would still be very difficult to carry out experimentally. One of the first problems to be approached is that of the flow of CSF between the intracranial cavity and vertebral canal. The results of simulation show, in this connection, that the flow of CSF between the intracranial cavity and vertebral canal takes place at a constant rate, as is apparent from the curves of blood volumes in the intracranial cavity. This rule governing the CSF flow is evidently explained by the fact of its nonlinear dependence of the pressure difference. Another distinctive feature of the CSF pressure dynamics in the vertebral canal is that the saturation time and shape of the curve are independent of the degree of increase of arterial pressure. The time taken to reach a steady level is likewise independent of the drop in venous pressure, which determines only the magnitude of the final pressure within the vertebral canal. Curves of the dynamics of blood volumes in the intracranial cavity, like those of the CSF pressures in the intracranial cavity and vertebral canal, have three characteristic parts. The first is characterized by a sharp increase in the volume of blood in the intracranial cavity, and its magnitude and duration of increase are determined entirely by the increase in venous pressure; this part of the curve coincides with an increase in ICP. Later, the ICP is maintained at a constant level, but because of the existence of a pressure difference between the intracranial cavity and vertebral
circulation
3.
Kt-
1.0 .-
0
;
6
12
1e
~. 20
24
Fig. 6. Dynamics of (a) intracranial pressure, (b) CSF pressure in vertebral canal, and (c) blood volume in intracranial cavity, for different values of hydraulic resistance to flow of CSF (kg).
canal there is a constant outflow of CSF from the cranium. The second part of the blood volume curve corresponds to this outflow, and the magnitude of the venous pressure drop determines its duration. The results of simulation show that the rate of flow of CSF between the intracranial cavity and vertebral canal has no effect on the final steady state of all the parameters investigated. It also has no effect on the first part of the curves, but its effect on the second part of the curves is considerable because the second part reflects the dynamics of the processes. An increase in the rate of flow, for instance, shortens the time required for stabilization of the ICP (Fig. 6, a) and lowers the level of the second part of the curves. The curves reflecting the dynamics of the CSF pressure in the vertebral canal (Fig. 6, b) show that an increase in the rate of flow of CSF results in the more rapid stabilization of the CSF pressure in the vertebral canal. A similar result is observed in the blood volume curves: the duration
412
1.4
Moskalenko
Am. Heart .I. March. 1972
et al.
t
r 0
4
6
1.2
16
20
24
0
4
2
12
16
26
24
1.4
t,
H..
1.4
1.0
0.6
t
,:,... 0
4
6
12
16
20
24
Fig. 7. Dynamics of (a) intracranial pressure, (b) CSF pressure in vertebral canal, and (c) blood volume in intracranial cavity, for different values of venous resistance (hi).
of the second part is dependent on the rate of flow of CSF. The other parameter of velocity which is an interesting topic for investigation, although difficult to test experimentally, is the rate of the venous outflow. This parameter depends on the hydraulic resistance of the venous system, which is exposed to the influence of the CSF system. Analysis of the simulation results shows that the hydraulic resistance of the venous system has a significant influence on all three parts of the ICP curve (Fig. 7, a), A decrease in the rate of outflow, caused by an increase in the hydraulic resistance, leads to an increase in the ICP level, and also to an increase in the time required to reach the second part. The difference between the stable levels of the second and third parts becomes more apparent as the rate of venous outflow falls. The dynamics of CSF pressure in the vertebral canal in this case (Fig. 7, b) is interesting because the initial part of the curves corresponds to a decrease of pressure, but later, regardless of the velocity
of outflow of blood, the curves are at first identical but then start to diverge. The initial decrease in CSF pressure in the vertebral canal is due to the fact that at the start pls > plc. The steady level of CSF pressure in the vertebral canal, like the ICP, depends on the rate of outflow of the blood. A family of curves reflecting the dynamics of the blood volume is shown in Fig. 7, c. These are interesting because the maximum of the first part, and the time taken to reach it, decrease with an increase in the rate of outflow of the venous blood. The total blood volume in the intracranial cavity also falls. The information concerning the velocities of CSF flow between the intracranial cavity and vertebral canal and of the venous outflow from the cranium obtained by analysis of the model as given above has not yet been confirmed by experimental data, but it points out a concrete way by which experimental proof is possible. By analysis of the model of the biophysical relationships in the intracranial circulatory system it is possible to examine those relationships which determine the influence of the state of this system on the intensity of the cerebral blood flow, which is extremely important both for the understanding of the mechanisms regulating the intracranial circulation under normal conditions and for the study of its disturbances in various pathological states. To solve this problem, certain modifications were introduced into the biophysical model of the intracranial circulatory system (Fig. 2) to enable its elements to be more precisely defined from the quantitative point of view. The vascular system of the brain was examined in accordance with Mchedlishvili’szg classification, represented as six divisions (regional, pial, and intracerebral arteries; capillaries, pial, and main veins) and their quantitative characteristics (mean radius, length, number of vessels) were introduced as for a dog weighing 6 to 8 kilograms. The results obtained by simulation are given in Fig. 8, a. Clearly the intensity of the cerebral blood flow is characterized by complex, nonlinear relationships during changes in the basic biophysical charac-
Volume Number
83 3
Biophysical
aspects of intracranial
be stabilized the arteries,
circulation
413
through a change in lumen of i.e., by active regulation.
Summary
240
160 80 0
Fig. 8. a, Volume velocity of blood flow as a function of arterial pressure and mean radius of resistive vessels; b, character of change in mean radius of resistive vessels during a change in arterial pressure to maintain blood flow at a constant level.
The first conclusion to be drawn from the data on fast and slow processesin the intracranial circulatory system and the results of their simulation described in this paper is that a sufficiently comprehensive group of data is now available for defining the biophysical structure of the intracranial circulatory system and for representing it by a functioning model, the investigation of which yields results that are in satisfactory agreement with the experimental data. As a result of investigation of such a model, as has been shown above, it is possible not only to clarify existing concepts of the mechanisms determining the dynamics of the principal biophysical characteristics of the intracranial circulatory system, but also to discover relationships not previously demonstrable by experimental methods. It is very important to note that analysis of the biophysical structure of the intracranial circulatory system also indicates those components which have been inadequately studied, thus setting the trend for future research. REFERENCES 1.
teristics of the intracranial circulatory system. Investigations of this model show, in particular, how the lumen of resistive vessels must change in order to stabilize the cerebral blood Aow when changes of arterial pressure occur (Fig. 8, b). It is very important to note that, as a result of simulation, the existence of unstable zones in the intracranial circulatory system has been discovered, both at certain values of the arterial, venous, and CSF pressures and also for certain values of the radius of the intracerebral arteries. Are these zones of instability the cause of acute disturbances of the cerebral blood flow in certain pathological states? It is difficult at present to say whether this is true or not, but at least it provides a concrete basis for further research in this direction. The characteristics obtained indicate that definite limits to changes in the biophysical parameters of the system exist, within which the cerebral blood flow can
2.
3.
4.
5.
6.
Moskalenko, Yu. E.: Dynamics of the blood volume of the brain under normal conditions and during gravitational loads, Leningrad, 1967, Nauka (Russ.). Moskalenko, Yu. E.: Telemetrical equipment for studying blood circulation of the brain, J. Physiol. 172:3, 1964. Moskalenko, Yu. E., and Naumenko, A.: Hemodynamics of cerebral circulation, in Cerebral ischemia, Springfield, Ill., 1964, Charles C Thomas, Publisher, p. 21. Dansker, V. L., Moskalenko, Yu. E., Sorokoumov, V. A., and Vainshtein, G. B.: Measurement of intracranial pressure and its pulse and respiratory fluctuations after intravenous injection of hypertonic solution, Fiziol. Zh. S.S.S.R. 54:1295, 1968 (Russ.). Demchenko, I. T.: Method of studying the local blood supply to the brain, Fiziol. Zh. S.S.S.R. 54:1123, 1968 (Russ.). Bellman, R., and Cooke, K. L.: Differentialdifference equations, New York and London, 1963, Academic Press. Mosso, A.: iiber Kreislauf des Blutes im menschlichen Gehirn. Leiozip. 1881. Veit & Coma. Geigel, R.: Die Rolle des Liquor cerebrospinaiis bei der Circulation im Schzdel, Pflueger. Arch. 109:337, 1905. Becher, E.: Untersuchungen iiber die Dynamik ,
IO,
,
414
IO.
11.
12. 13. 14.
15.
16. 17.
18. 19.
Moskalenko
et (11.
des Liquor cerebrospinalis, Mitt. Grenzgeb. Med. Chir. 35:366, 1922. Kedrov, A. A., and Naumenko, A. I.: Problems in physiology of the intracranial circulation with their clinical interpretation, Leningrad, 19.54, Medgiz (Russ.). Vasilevskii, N. N., and Naumenko, A. I.: Velocity of the cerebral blood flow and movement of the cerebrosoinal fluid, Leningrad, 1959, Medgiz (Russ.). * Vainshtein, G. B.: Origin of the respiratory waves of intracranial pressure, Fiziol. Zh. S.S.S.R. 55:1253, 1969 (Russ.). Flexner, L. B., Clark, J. H., and Weed, L. H.: The elasticity of the dural sac and its contents, Amer. J. Physiol. 102:292, 1932. Moskalenko, Yu. E., and Naumenko, A. I.: Investigation of the character of CSF movement in normal animals, Fiziol. Zh. S.S.S.R. 45:562, 1959 (Russ.). Kislyakov, Yu. Ya. : Mathematical simulation of intracranial hemodynamics by the method of finite differences, Biofizika 14:179, 1969 (Russ.). Bergel, D. H.: The static elastic properties of the arterial wall. I. Phvsiol. 156:445, 1961. Savitskii, N. N.1 Biopdysicai basis of the circulation of the blood and clinical methods of study of the hemodynamics, Leningrad, 1963, Publisher Medgiz (Russ.). Rashevsky, N.ySome medical aspects of mathematical biology, Springfield, Ill., 1964, Charles C Thomas, Publisher. Kiselev, P. G.: Hydraulics, Leningrad, 1963, Publisher Gosenergoisdat (Russ.).
Am. Heart J. March, 1972
20. Bering, E. A.: Choroid plexus and arterial pulsation of cerebrospinal fluid, Arch. Neurol. Psychiat. 73:165, 1955. 21. Hamit, H. F., Beall, A. C., and De Bakey, M. E.: Hemodynamic influences upon brain and CSF; pulsations and pressures, J. Trauma 5:174, 1965. 22. Adolph, R. J., Fukusumi, H., and Fower, N. 0.: Origin of cerebrospinal fluid pulsations, Amer. J. Physiol. 212:840, 1967. 23. Jenkner, F. L.: Rheo-encephalography, Springfield, Ill., 1962, Charles C Thomas, Publisher. 24. Namon, R., Gallan, F., Schimojo, S., Sano, R. M., Markovich, S. E., and Scheinberg, P.: Basic study in rheoencephalography, Neurology 17:239, 1967. 25. Yarulin, Kh. Kh.: Diagnosis of pathological tortuosity of the carotid arteries by rheoencephalography, Zh. Nevropat. Psikhiat. 65: 1476, 1965 (Russ.). 26. Klosovskii, V. N.: Circulation of blood in the brain, Moscow, 1951 (Russ.). Translation: Office of Technical Service, Washington, 1963, U. S. Dept. of Commerce. 27. Grodins, F. S.: Control theory and biological systems, New York, 1963, Columbia University Press. 28. Milsum, J. H.: Biological control system analysis, New York, 1966, McGraw-Hill Book Co., Inc. 29. Mchedlishvili, G. I.: Functions of the vascular mechanisms of the brain, Leningrad, 1968, Naukoi, publisher. (Russ.).