**2. The role of skull pulse expanding in mechanism of circulatory supply of brain function**

The system of cerebral metabolic supply is dependent on the interaction of a number of elements some of them are determined by the skull properties. One of the most significant in this direction is clarifying the role of CSF movement to this system inside cranium and significance at this process of the bio-mechanical properties of the skull. Critical position in the role of the skull in support of circulatory-metabolic supply of brain functioning determined by the ability of the skull to accept an additional volume of blood during the phase of systolic increase in central arterial pressure.

Indeed, arterial blood pressure consists of two components. One is the steady state of flow through the brain, determined by the basal tone of the brain blood vessels. The second occurs with each heart- beat, which initiated by arterial pressure increases and so drives the pulse volume into the cranium. It is this component that is influenced by the level of cranial compliance, which in turn depends on the volume flexibility of the skull.

This increase in arterial pressure is short – about 0.1s. This means that the cranium needs to accommodate the increase in systolic blood volume very quickly in order to use it to drive cerebral circulation. This possibility, predicted by mathematical simulation of the cerebrovascular system [12], should be follow from biomechanical properties of the skull as united bio-mechanical system.

### 66 Injury and Skeletal Biomechanics

That is important statements, because from the beginning of XIX Century up to the second part of XX Century the most of investigators belong to conception, named "Monroe-Kelly" doctrine, which on the base of majority of anatomical investigations, declare, that skull is fully rigid cavity. However, when this statement has been included to the model, it didn't function. However, when some possibility for pulse change of intracranial volume has been included to the model, it starts to work. It was the first indicator, which shows the importance of pulse change of internal skull cavity. Some years later the presence of pulse dependence on "Pressure-Volume" relation for the skull have been shown by invasive technique [13].

The Role of Skull Mechanics in Mechanism of Cerebral Circulation 67

**3-5ml of stroke volume**

*and CSF - mobility*

*Depends on expanding of skull*

**6-7ml of stroke volume**

**(Pulsatile blood flow)**

*Depends on Vascular Resistance*

**(Steady state blood flow)**

**Figure 1.** Distribution of steady state and fluctuating of stroke volume at normal physiological

CSF pressure, which is a real source of forces for brain expanding.

This means, that through an average sized human brain (1200g) – about 600ml flows every minute and 110-130 ml of blood is about 20% of total brain blood supply. In case of skull is completely rigid, this additional stroke volume will by out from cerebral circulation, because additional blood couldn't inflow to the skull due to contra-pressure, determined by unchangeable volume of cranial cavity. Therefore, brain blood flow may be diminished up to 15-20%. Direct evidence of the presence of pulse skull expanding have been received by coupling of Rheoencephalogram (REG) – method, based on recording of electrical impedance between electrodes, placed in fronto-mastoid position to human head and transcranial dopplerogram (TCD) of basement of the Middle Cerebral artery [17). REG reflect changes of intracranial blood/CSF volume, because electrical resistance of these media are significantly less to compare with brain tissue and pulse blood volume fluctuations inside skull if they are have taken place, will change common electrical resistance between electrodes [14]. TCD reflect pulse changes of linear velocity inside intracranial large arteries [18], which by Poiseuille low are proportional to volume fluctuations of these arteries, surrounded by CSF. Volume fluctuations of large brain arteries could be compensated by skull expanding due to transmitting of arterial to surrounding

Computed aid analysis of simultaneously recorded REG and TCD pulse give the possibility to establish "Pressure-Volume" dependence for the skull for systolic phase of pulse cycle [17], which show, that this dependence is nearly to linear and in normalized coordinates equal to line with angle to horizontal coordinate 30-40o(Fig.2a) Linearity at the most cases of this dependence indicate, that pulse changes of intracranial pressure and volume are linear, which is permits to conclude, that SCF replacements inside skull during systolic part of cardiac cycle practically absent. Therefore, the fact of the presence of systolic skull pulse expansion has taken place and it is one of element of mechanism, which is responsible for circulatory-metabolic support of brain functioning and is possible quantitative to express as

conditions.

**100**

**cm/s**

**(∆P)**

**TCDG**

**80**

**60**

**40**

**20**

**0**

Follow this data, the skull could be accepted as a nearly rigid container with limited capabilities to accommodate internal volume changes in response to increases in arterial pressure. However, because investigations of Marmarou have been provided when comparative slow changes of intracranial pressure as respond to infusion to the skull artificial CSF, when volume compensation is provided also by CSF outflow to some spaces, connected with the skull by comparatively narrow gapes spinal cord, volumes, determined by arachnoid membranes of cranial nerves.

Therefore, it was important to evaluate skull itself volume reserves, in other words dynamic skull volume capabilities. Really, it is important to have the possibility to accept by the skull an extra volume of blood following the systolic increase in arterial pressure, which is in addition to the steady state level of the brain blood flow. The most rapid component of change of arterial blood pressure is evoked in systolic phase duration about 0.1s. During this time any replacements of CSF inside skull couldn't be provided [14].

There are skull expansions due to, perhaps, articular comparative mobility of skull bone in sutures of invisible value; investigations have shown, that these changes of articular bone position are less then 0.5 geometric degree [15], and this, as it follows from calculation, could increase internal volume of skull up to 3-6 ml.

Calculation of additional – systolic blood volume, which should accept cranial cavity may be provided, taking into account, than brain "portion" of stroke volume is about 10 ml. That is means, that steady stroke volume is 5 -7 ml and pulse component is 5-3 ml (Fig.1). Namely this the last volume of blood should accepted by skull during systolic phase of cardiac cycle. Comparatively to total volume of cranial cavity this volume is very small. Averaged size human brain is about 1200 ml. This value should be closely to internal volume of the skull. This means, that expand of internal volume of skull about 0.3% of initial volume to accept systolic portion of blood, could give the additional blood, which is necessary for normal functioning of circulatory –metabolic brain supply. Taking into account, that heart rate is usually 60-70 beats per minute, this additional blood volume will be about pulse evaluation due to of skull expanding could be about 110-130 ml per minute. It is known, that normal brain blood made using some relatively simple calculations. As well it was established in the middle of the last Century, brain takes 50-65ml of blood volume flows through 100g of brain mass in 1 minute [16].

66 Injury and Skeletal Biomechanics

technique [13].

by arachnoid membranes of cranial nerves.

That is important statements, because from the beginning of XIX Century up to the second part of XX Century the most of investigators belong to conception, named "Monroe-Kelly" doctrine, which on the base of majority of anatomical investigations, declare, that skull is fully rigid cavity. However, when this statement has been included to the model, it didn't function. However, when some possibility for pulse change of intracranial volume has been included to the model, it starts to work. It was the first indicator, which shows the importance of pulse change of internal skull cavity. Some years later the presence of pulse dependence on "Pressure-Volume" relation for the skull have been shown by invasive

Follow this data, the skull could be accepted as a nearly rigid container with limited capabilities to accommodate internal volume changes in response to increases in arterial pressure. However, because investigations of Marmarou have been provided when comparative slow changes of intracranial pressure as respond to infusion to the skull artificial CSF, when volume compensation is provided also by CSF outflow to some spaces, connected with the skull by comparatively narrow gapes spinal cord, volumes, determined

Therefore, it was important to evaluate skull itself volume reserves, in other words dynamic skull volume capabilities. Really, it is important to have the possibility to accept by the skull an extra volume of blood following the systolic increase in arterial pressure, which is in addition to the steady state level of the brain blood flow. The most rapid component of change of arterial blood pressure is evoked in systolic phase duration about 0.1s. During this

There are skull expansions due to, perhaps, articular comparative mobility of skull bone in sutures of invisible value; investigations have shown, that these changes of articular bone position are less then 0.5 geometric degree [15], and this, as it follows from calculation,

Calculation of additional – systolic blood volume, which should accept cranial cavity may be provided, taking into account, than brain "portion" of stroke volume is about 10 ml. That is means, that steady stroke volume is 5 -7 ml and pulse component is 5-3 ml (Fig.1). Namely this the last volume of blood should accepted by skull during systolic phase of cardiac cycle. Comparatively to total volume of cranial cavity this volume is very small. Averaged size human brain is about 1200 ml. This value should be closely to internal volume of the skull. This means, that expand of internal volume of skull about 0.3% of initial volume to accept systolic portion of blood, could give the additional blood, which is necessary for normal functioning of circulatory –metabolic brain supply. Taking into account, that heart rate is usually 60-70 beats per minute, this additional blood volume will be about pulse evaluation due to of skull expanding could be about 110-130 ml per minute. It is known, that normal brain blood made using some relatively simple calculations. As well it was established in the middle of the last Century, brain takes 50-65ml of blood volume flows through 100g of

time any replacements of CSF inside skull couldn't be provided [14].

could increase internal volume of skull up to 3-6 ml.

brain mass in 1 minute [16].

**Figure 1.** Distribution of steady state and fluctuating of stroke volume at normal physiological conditions.

This means, that through an average sized human brain (1200g) – about 600ml flows every minute and 110-130 ml of blood is about 20% of total brain blood supply. In case of skull is completely rigid, this additional stroke volume will by out from cerebral circulation, because additional blood couldn't inflow to the skull due to contra-pressure, determined by unchangeable volume of cranial cavity. Therefore, brain blood flow may be diminished up to 15-20%. Direct evidence of the presence of pulse skull expanding have been received by coupling of Rheoencephalogram (REG) – method, based on recording of electrical impedance between electrodes, placed in fronto-mastoid position to human head and transcranial dopplerogram (TCD) of basement of the Middle Cerebral artery [17). REG reflect changes of intracranial blood/CSF volume, because electrical resistance of these media are significantly less to compare with brain tissue and pulse blood volume fluctuations inside skull if they are have taken place, will change common electrical resistance between electrodes [14]. TCD reflect pulse changes of linear velocity inside intracranial large arteries [18], which by Poiseuille low are proportional to volume fluctuations of these arteries, surrounded by CSF. Volume fluctuations of large brain arteries could be compensated by skull expanding due to transmitting of arterial to surrounding CSF pressure, which is a real source of forces for brain expanding.

Computed aid analysis of simultaneously recorded REG and TCD pulse give the possibility to establish "Pressure-Volume" dependence for the skull for systolic phase of pulse cycle [17], which show, that this dependence is nearly to linear and in normalized coordinates equal to line with angle to horizontal coordinate 30-40o(Fig.2a) Linearity at the most cases of this dependence indicate, that pulse changes of intracranial pressure and volume are linear, which is permits to conclude, that SCF replacements inside skull during systolic part of cardiac cycle practically absent. Therefore, the fact of the presence of systolic skull pulse expansion has taken place and it is one of element of mechanism, which is responsible for circulatory-metabolic support of brain functioning and is possible quantitative to express as value of Tang. of angle of "Pressure-Volume" dependence in normalized coordinates. This dependence corresponds also to meaning "Cranial Compliance", applied to systolic phase of cardiac cycle, or in other words, "Dynamic Cranial Compliance" (DCC). Direct evidence of the role of small increasing of intracranial volume to DCC have been received by observation on neurosurgical patients just before and after trepanation, provided for the next neurosurgery [19]. These investigation have shown, that small 6-10cm2 "window" in skull bone with saved brain cover membrane, when real intracranial volume increase to a few (3-6 ml) due to deformation of brain cover membrane, could change significantly DCC (Fig.3). The significance of this mechanism was confirmed during many years experience in skull trepanation, which is used for increase of intracranial volume up to the present time.

The Role of Skull Mechanics in Mechanism of Cerebral Circulation 69

brain mass, which have been shown by MRI investigations [22]. Investigations, provided with aging persons, after 65-70 by comparing results of blood flow measurements, and DCC measurements and determination level of dementia level by psychophysiological computerized method "Prognosis", show (Fig. 4), that level of decrease of cognitive brain function and DCC are proportional but not closely correlate with values of level of brain blood that even small [17]. It is possible to conclude, that biomechanical properties of the skull determine its expanding due to pulse increase of intracranial pressure permits to accept additional volume of blood during systolic increase of central arterial pressure, with play sometimes significant role in supporting circulatory-metabolic supply of brain

**Figure 4.** Dependence between value of DCC , Cerebral blood flow and CSF – mobility in aging human

During diastolic part of cardiac cycle biomechanical properties of the skull also play role in supporting of cerebral blood circulation due to energy, collected during systolic increase of central arterial pressure. In this phase the role of CSF replacements is increase. In the beginning, they, in coupling with skull biomechanics, provide the distribution of pulse blood volume inside skull and, then, support pulse outflow of venous blood from the skull. Thus, evaluation of DCC for the skull during each cardiac cycle is comprised of the initial interval as a rapid and nearly linear increase of arterial pulse pressure which lasts from 0.05 - 0.15s and perfectly reflects "Pressure-Volume." dependence, or DCC, which is determined by the equivalent elasticity of the cranium due to the biomechanical of the skull structure

groups which are different by level of cognitive disfunction.

functioning.

elements

**Figure 2.** Averaged changes of DCC for different age groups, showing the decline in CCe in the middleage group.

**Figure 3.** Averaged DCC values before and after trepanation. Changes in the biomechanical elasticity of the skull allow the cranium to accept additional blood with each pulse stroke.

All above data permits to conclude, that without property of rapid expanding of the skull when DCC =0, brain blood flow will decrease with the same indices of arterial and venous central pressure to significant value – up to 15-20%., which is significant for brain functioning. The known data shows, that even some less significant decrease of DCC may in some cases reflect to brain activity. This suggestion is confirmed by observations, which shows, that DCC gradually decrease up to age 40-50 and, then increase again-Fig. 2b,c [20]. That abnormal decrease of angle of normalized curve widely vary for different persons and its pronounced values are correlate with some neurological symptoms (headache, decreased working capabilities). It is important to mention, that an increase of DCC after 55-60 Years (Fig.2c) is not connected with the skull properties. It is determining by aging decrease of brain mass, which have been shown by MRI investigations [22]. Investigations, provided with aging persons, after 65-70 by comparing results of blood flow measurements, and DCC measurements and determination level of dementia level by psychophysiological computerized method "Prognosis", show (Fig. 4), that level of decrease of cognitive brain function and DCC are proportional but not closely correlate with values of level of brain blood that even small [17]. It is possible to conclude, that biomechanical properties of the skull determine its expanding due to pulse increase of intracranial pressure permits to accept additional volume of blood during systolic increase of central arterial pressure, with play sometimes significant role in supporting circulatory-metabolic supply of brain functioning.

68 Injury and Skeletal Biomechanics

∆**V 1.0**

**0.5**

**0**

age group.

value of Tang. of angle of "Pressure-Volume" dependence in normalized coordinates. This dependence corresponds also to meaning "Cranial Compliance", applied to systolic phase of cardiac cycle, or in other words, "Dynamic Cranial Compliance" (DCC). Direct evidence of the role of small increasing of intracranial volume to DCC have been received by observation on neurosurgical patients just before and after trepanation, provided for the next neurosurgery [19]. These investigation have shown, that small 6-10cm2 "window" in skull bone with saved brain cover membrane, when real intracranial volume increase to a few (3-6 ml) due to deformation of brain cover membrane, could change significantly DCC (Fig.3). The significance of this mechanism was confirmed during many years experience in skull trepanation, which is used for increase of intracranial volume up to the present time.

**Figure 2.** Averaged changes of DCC for different age groups, showing the decline in CCe in the middle-

**0.5**

**0.5 1.0 0.5 1.0**

**CCe=1,26±023 CCe=0,69±0,16 CCe=0,78±0,18**

**1.0**

**0 0**

∆**V** ∆**V**

**0.5**

<sup>∆</sup>**<sup>P</sup>** <sup>∆</sup>**<sup>P</sup>**

**1.0**

**Age: 18-25 40-50 65-75**

**0.5**

**1.0**

∆**P**

**Figure 3.** Averaged DCC values before and after trepanation. Changes in the biomechanical elasticity of

All above data permits to conclude, that without property of rapid expanding of the skull when DCC =0, brain blood flow will decrease with the same indices of arterial and venous central pressure to significant value – up to 15-20%., which is significant for brain functioning. The known data shows, that even some less significant decrease of DCC may in some cases reflect to brain activity. This suggestion is confirmed by observations, which shows, that DCC gradually decrease up to age 40-50 and, then increase again-Fig. 2b,c [20]. That abnormal decrease of angle of normalized curve widely vary for different persons and its pronounced values are correlate with some neurological symptoms (headache, decreased working capabilities). It is important to mention, that an increase of DCC after 55-60 Years (Fig.2c) is not connected with the skull properties. It is determining by aging decrease of

the skull allow the cranium to accept additional blood with each pulse stroke.

**Figure 4.** Dependence between value of DCC , Cerebral blood flow and CSF – mobility in aging human groups which are different by level of cognitive disfunction.

During diastolic part of cardiac cycle biomechanical properties of the skull also play role in supporting of cerebral blood circulation due to energy, collected during systolic increase of central arterial pressure. In this phase the role of CSF replacements is increase. In the beginning, they, in coupling with skull biomechanics, provide the distribution of pulse blood volume inside skull and, then, support pulse outflow of venous blood from the skull.

Thus, evaluation of DCC for the skull during each cardiac cycle is comprised of the initial interval as a rapid and nearly linear increase of arterial pulse pressure which lasts from 0.05 - 0.15s and perfectly reflects "Pressure-Volume." dependence, or DCC, which is determined by the equivalent elasticity of the cranium due to the biomechanical of the skull structure elements

It is important to emphasize that changes of the steady component of brain blood flow, determined by the perfusion pressure, are independent of the pulsatile component. The total brain blood supply is determined by the superposition of the steady state perfusion pressure (average level of arterial pressure) and the components of blood flow, which are in turn determined by the biomechanical properties of the skull and the mobility of cerebrospinal fluid within the skull.

The Role of Skull Mechanics in Mechanism of Cerebral Circulation 71

on the base of modern technology, have been appeared at the end of XX Century. Firstly, direct observations demonstrated, that skull represents a complicated mechanical moveable system. This suggestion is based on investigations, represented device with needles inserted through cover skull tissues in human head and fixed in skull bone. Invisible movements of upper end of the needle were registered by means of small mirror fixed there, which are

**Figure 5.** Principle of transforming individual regions of image series into the amplitude-time plot: (a) input of the image series into a computer and specification of the analyzed region; (b) collocation of images and creation of the intermediate image; and (c) transformation of the intermediate image into

deflected laser beam, focused to the mirror [28].

the amplitude-time plot.
