cerebral hemodynamics and cerebrospinal fluid flow in the ... · martin strama* ian gould ......

Fall 2013 Biological Systems Analysis

Cerebral Hemodynamics and Cerebrospinal Fluid Flow in the

Presence of Choroid Plexus Papilloma

Martin Strama* Ian Gould

Chih-Yang Hsu Andreas Linninger

Abstract Quantification of the cerebrospinal fluid (CSF) system may be useful for distinguishing relative treatments in the presence

of choroid plexus papillomas (CPPs). To study the CSF system, mathematical models and simulations detailing the

cerebral blood flow and CSF filtration were constructed to represent a normal brain, a brain with CPP located in the left

lateral ventricle, and a brain with CPP located in the fourth ventricle. Furthermore, analysis of treatments by implementing

a shunt for each experimental case were assessed. Flow distributions and intracranial pressures were obtained to assess

the severity of each condition and the effectiveness of the shunt treatments. The results show that when CPP grows in the

LLV or in the 4V, the ICP grows uncontrollably. When the shunt is applied to the LLV, the shunt is most effective after

about 40% CPP growth. When the shunt is applied to the 4V, the shunt is effective from the very onset of CPP growth.

Keywords

Choroid plexus papilloma Cerebrospinal fluid Cerebral hemodynamics Intracranial pressure Computational

flow rates Mathematical modeling

Martin Strama

[email protected]

Department of Bioengineering

College of Engineering, College of Medicine

University of Illinois at Chicago, Chicago, USA

Ian Gould Chih-Yang Hsu Andreas Linninger

Laboratory for Product and Process Design (LPPD)

Department of Bioengineering

College of Engineering, College of Medicine

University of Illinois at Chicago, Chicago, USA

Cerebral hemodynamics and cerebrospinal fluid flow in the presence of choroid plexus papilloma 2

Table of Contents

Section I: Introduction

Motivation ……………………………………………………………………………………………………………………… 3

Background

Cerebral Vasculature Circulation …………………………………………………………………………………........ 3

Cerebrospinal Fluid Production ………………………………………………………………………………………… 4

Cerebral Spinal Fluid Circulation ………………………………………………………………………………………. 4

Outline ………………………………………………………………………………………………………………………….. 5

Section II: Methods

Overview of Model Simulation ………………………………………………………………………………………………. 5

Assumptions ……………………………………………………………………………………………………………………. 5

Mathematical Basis ……………………………………………………………………………………………….................. 5

Boundary Conditions ……………………………………………………………………………………………................... 6

Optimizations …………………………………………………………………………………………………….................... 6

Sensitivity Analysis on Microvasculature Resistance ………………………………………………………………… 6

Establishing CSF Flow …………………………………………………………………………………………………… 7

ICP Determination ………………………………………………………………………………………………………… 7

Model Simulations ……………………………………………………………………………………………….................... 7

Section III: Results

ICP Profiles ………………………………………………………………………………………………………................... 9

Conservation of CSF Flow ………………………………………………………………………………………................. 9

Simulation Results

ICP Dynamics ……………………………………………………………………………………………………………… 11

CPP in the L LV without Shunt ………………………………………………………………………………………….. 13

CPP in the L LV with Shunt ………………………………………………………………………………….................. 13

CPP in the 4V without Shunt …………………………………………………………………………………................ 13

CPP in the 4V with Shunt …………………………………………………………………………………….................. 13

CSF Flow Distribution Schematics ……………………………………………………………………………………… 13

Section IV: Discussion ……………………………………………………………………………………………..... 13

Section V: Conclusion ………………………………………………………………………………………………. 17

References ……………………………………………………………………………………………………………. 17

Abbreviations

CPP Choroid Plexus Papilloma

Cerebrospinal Fluid System Cerebral Hemodynamic System

CSF Cerebrospinal Fluid LICA Left Internal Carotid Artery

LLV Left Lateral Ventricle RICA Right Internal Carotid Artery

RLV Right Lateral Ventricle BA Basilar Artery

3V Third Ventricle LJV Left Jugular Vein

4V Fourth Ventricle RJV Right Jugular Vein

AV Arachnoid Villi

ICP Intracranial Pressure

M. Strama et al. 3

1. Introduction

1.1 Motivation

Choroid plexus papillomas (CPPs) are benign neuroepithelial intraventricular tumors accounting for approximately 1%

of all verified intracranial neoplasms [1,2]. Approximately, 85% of all CPPs occur in children under the age of five, 2-6%

of all pediatric brain tumors, and 0.5% of adult brain tumors [1]. CPPs arise from the choroid plexus (CP), a richly

vascularized tissue situated in the roof of each of the four brain ventricles [3]. Frequent locations of CPPs are the lateral and

third ventricles (LV, 3V) in children and the fourth ventricle (4V) in adults [2]. CPPs invade nearby tissue and spread widely

via the cerebrospinal fluid (CSF) [4]. Although benign, CPPs obstruct CSF flow, which leads to increased CSF production

by the CP thus causing increased intracranial pressure (ICP) and hydrocephalus [4]. While the CPPs effect of compressing

brain tissue and increasing CSF production is well described clinically, the brain analysis as a system of cerebral

hemodynamics in the presence of CPPs are poorly understood. The following paper aims to: (i) analyze CSF flow patterns

inside the ventricular and subarachnoidal regions during CPP growth; and (ii) analyze the auto-regulation mechanisms of

the CSF system during treatment of CPP via insertion of a shunt.

1.2 Background

1.2.1 Cerebral Vasculature Circulation

Blood continuously circulates in the brain to allow for stable perfusion in order to maintain its function as shown in

Figure 1 [10,11]. Total blood flow through the human brain is approximately 750 ml min-1 [10]. The latter implies that the

cerebral circulation receives 15-20% of cardiac output, which at rest is 5000 ml min-1, whose mass is only about 2% of the

total body weight [10,11]. The Circle of Willis (CoW), a ring-like network of collateral vessels, is the main cerebral

distribution center for blood flow [11]. The left internal carotid artery (LICA) and the right internal carotid artery (RICA)

of the CoW contribute roughly 50-80% of the cerebral blood supply. Two vertebral arteries that join intracranially to form

the basilar artery (BA) account for the rest of the cerebral blood supply. The LICA and RICA each branch to form the

middle cerebral arteries and anterior cerebral arteries that circulate blood to the frontal, temporal, and parietal regions of the

brain. The occipital lobe, cerebellum, and the brain stem receive blood from the right posterior cerebral artery and the left

posterior cerebral artery which result from the bifurcation of the BA [11].

The main physiological hemodynamic parameter characterizing the central circulation in the brain is the arteriovenous

pressure difference [10]. The central arterial pressure and the central venous pressure are the two parameters used to describe

the central circulation. The two parameters must be maintained at constant levels in an organism under normal conditions.

The control of blood flow to the brain is determined by alterations in the vascular resistance, which in turn induces the

respective blood flow, pressure, and volume changes in the cerebral vascular bed [10].

Figure 1 [12]. Ventral view of the brain. Two pairs of arteries supply blood to the brain: the vertebral arteries and the internal carotid

arteries. The vertebral arteries converge to form the basilar artery. A ring of connected arteries lies at the base of the brain. The ring is

called the circle of Willis.


1.2.2 Cerebrospinal Fluid Production

One of the main functions of the CP is to produce and secrete CSF from the epithelial cells. CSF fills the ventricles of

the brain and the spaces of the central nervous system. The CSF volume in humans is 140 mL and is replaced four times a

day for an overall volume of approximately 600 ml per day [5]. The production of CSF is dependent on the fluid transfer

between blood vessels and into the epithelial cells [3]. The rate of CSF secretion is constant at approximately 200 l min-1

per gram of CP tissue. In humans, the CP weigh approximately 2 grams total making the rate of CSF secretion to be between

320 to 400 l min-1 [5,6].

The CP also act to maintain homeostasis of the brain environment by acting as a barrier interface between blood and

CSF [3]. Composed of numerous villi that project into the ventricles of the brain, the CP forms the blood-CSF barrier

(BCSFB) by the epithelial cells, which are linked together by tight junctional complexes. Epithelial cells contain a large

surface area which means that the total surface are of the BCSFB is on the same order of magnitude as that of the blood-

brain barrier [5]. As a result of the BCSFB, the CP constantly regulates the composition of the CSF. An estimated of 10-

30% of total CSF production is generated by the convection (bulk flow) of interstitial fluid from the brain parenchyma to

the ventricles and subarachnoid space (SAS) [7]. Compared to other regions in the brain, blood flow to the CP is higher in

order to maintain a continuous CSF production at a relatively high rate [7]. The large surface area of the epithelium helps

support the high rate of CSF secretion by the CP.

The basal lamina, the layer of extracellular matrix secreted by the epithelial cells, acts as a barrier to the migration of

cells during normal development. The basal lamina also acts as a track for the migration of tumor cells [8]. In CCP, the

basal lamina extends linearly from its usual perivascular site along the bases of tumors cells. Several sheets of the basal

lamina secrete, more or less in parallel, forming masses 2-20 mm in size [9].

1.2.3 Cerebrospinal Fluid Circulation

During systole, contraction of the heart, arterial blood flows into the tissues of the CP causing the CP to expand and

secrete CSF at a constant rate. The CP behaves as a pump supplying the kinetic energy to drive CSF circulation [6]. CSF

flows rapidly through the ventricles, subarachnoid cisterns, and perivascular spaces as show in Figure 2. CSF diffuses more

slowly in the interstitial spaces into the brain parenchyma, reaching every location in the brain [14]. More specifically, CSF

flows sequentially through two lateral ventricles (LLV and RLV), the foramina of Monro, the third ventricle (3V), and into

A

B

C

Figure 2 [13]. A. The human ventricular system of the brain is a set of four chambers where cerebrospinal fluid (CSF) flows. B. CSF is

produced by the choroid plexuses (CP) located within each ventricle. C. CSF flows from the lateral and third ventricles to the fourth

ventricle via cerebral aqueduct. CSF circulates around the spinal cord and brain in the subarachnoid space (SAS) to empty into the

superior sagittal sinus via arachnoid granulations.

M. Strama et al. 5

the fourth ventricle (4V) through the aqueduct of Sylvius [6]. CSF then reaches the SAS through the foramina of Luschke

and Magendie where it is reabsorbed through the arachnoid villi (AV) at the sagittal sinus (SS) into the venous system [6].

1.3 Outline

Section one helped develop the necessary physiological foundation needed to being addressing the following aims: (i)

analyze CSF flow patterns inside the ventricular and subarachnoidal regions during CPP growth; and (ii) analyze the auto-

regulation mechanisms of the CSF system during treatment of CPP via insertion of a shunt. Section two introduces the

mathematical basis and equations describing the blood and CSF flow in the model. The development of the model being

utilized is presented along with the specific simulations being conducted. Results are presented in section three for ICP

values and CSF flow rates for each simulation performed. Section four discusses the validity of the results with clinical

observations. Section five highlights the overall gain from these simulations for use in future clinical applications of shunts

for CPP treatment.

2. Methods

2.1 Overview of Model Simulation

To help obtain a better understanding of cerebral hemodynamics and CSF flow patterns during CPP growth, a steady-

state model of intracranial dynamics was designed as shown in Figure 3. The model accounts for the interaction between

the cerebral vascular system and the CSF system. The cerebral vascular system is divided into arteries, capillaries

(microvessels), and veins. The CSF system includes: LLV, RLV, 3V, 4V, the CPs, the choroid arteries, and the cerebral and

subarachnoid spaces (arachnoid villi, AV) which are all connected.

2.2 Assumptions

The following assumptions are semi-standard in one-dimensional cylindrical-tube hemodynamics and are applied to

this model: (i) blood is viscous and the density is constant which indicates that blood is incompressible; (ii) the flow is

steady, laminar, and uniform which indicates that pressure, shear stress, and velocity do not change with respect to time;

(iii) the flow is fully developed which indicates that velocity depends upon axial distance along the channel, not the entrance

length; (iv) edge effects are neglected; and (v) blood is assumed to behave as a Newtonian fluid [16].

2.3 Mathematical Basis

This model transforms the cerebral vascular system and the CSF system into a circuit network where a conservation

balance shown in Equation 1 dominates.

Flow Flow External

AccumulationIn Out Forces

(1)

Assuming that no accumulation as well as no external forces such as reactions occur in the model, a simple conservation

equation occurs as shown in Equation 2.

A

B

Figure 3 [15]. Based on the anatomy and physiology of the human brain from Figure 1 and Figure 2 (A), the cerebral vasculature system

and the CSF system were modeled as simplified pipe networks (B). The miscellaneous microcirculation of the brain were compacted

into compartments since they are not of primary focus.


, ,

n n

i in i out

i i

f f

(2)

Equation 4 emphasizes that the sum of the inlet

flows into the model equals the sum of the outlet

flows from the model, and the net flow to a node

is zero.

To solve for pressures, the constitutive

Hagen-Poiseuille equation will be utilized to

complement each conservation of flow

equation. The Hagen-Poiseuille Law gives the

pressure drop P in a fluid f flowing through a

long cylindrical pipe with resistance α as shown

in Equation 3 and Equation 4:

P f (3)

where

with being the viscosity of the fluid, L being the length of the cylindrical tube, and D being the diameter of the of the

cylindrical tube.

Fluid flow in the model flows from areas of high pressure to areas of low pressure between the three inlet pressures of

the RICA, LICA, and BA to the two outlet pressures of the jugular veins (LJV, RJV). As a result, there is a pressure gradient

from the arterial pressures to the venous pressures where pressures decrease from arterial to venous.

2.4 Boundary Conditions

The model contains three main artery inputs: RICA, LICA, and BA. Cerebral perfusion pressure is the difference

between intra-arterial pressure and pressure in the veins. Cerebral perfusion pressure ranges from 60-160 mmHg. A cerebral

perfusion pressure of 100 mmHg has been used in research and literature for models of this type and will be utilized as the

input pressure for the RICA, LICA and BA [10,17,18]. Venous pressure is normally low with values between 2-5 mmHg

and is influenced directly by intracranial pressure (ICP). ICP quantifies the pressure in the skull and thus in the brain tissue

and CSF. ICP is normally between 7-15 mmHg [19]. Venous pressures of 3 mmHg have been used as well in prior models

and will be utilized as the output pressure for the LJV and RJV [17,18]. Actual values of pressures may fluctuate from one

artery to another and from one vein to another in the brain. Table 1 summarizes the given initial conditions as well as

additional information used for the simulation of the model.

2.5 Optimizations

The complexity of the brain cannot be stressed enough. The network model for the cerebral vasculature system and CSF

system shown in Figure 3 is a well-structured, simplified assumption of the actual human brain. When preliminary

simulations on the normal brain state with no CPP were conducted, inaccurate cerebral blood flow rates resulted in the

RICA, LICA, and BA as compared to measured physiological data [10,20].

2.5.1 Sensitivity Analysis on Microvasculature Resistance

The original network model was insufficient in accurately analyzing the hemodynamics of the cerebral vasculature.

After further analysis of the network model, the simulation data showed that the resistance in the microvasculature directly

affected the total cerebral blood flow. Numerous vessels containing very small diameters, the microvasculature has a

significantly high resistance that directly impacts the total cerebral blood flow entering and exiting the brain. Figure 4 (page

7) shows the sensitivity analysis of the resistance of the microvasculature system in the brain in order to obtain the correct

cerebral blood flow of 750 ml min-1. Table 2 (page 7) summarizes the effects of reducing the resistance of the

microvasculature on the inlet arteries and outlet veins for blood circulation. As the degree of microvasculature reduction

increases, the blood flow through the BA, RICA, LICA, RJV, and LJV increase. The goal is to find a resistance reduction

where the sums of the three inlet arteries equals the physiological value of 750 ml min-1. The sensitivity analysis concludes

that a 77.4% reduction of the resistance in the microvasculature will result in physiological accepted cerebral blood flows.

4

128 L

D

(4)

Table 1 Material Properties for Model

Location Property, Variable Unit(s) Value Reference

R ICA Pressure, Pin,RICA mmHg 100 [10,17,18]

L ICA Pressure, Pin,LICA mmHg 100 [10,17,18]

BA Pressure, Pin,BA mmHg 100 [10,17,18]

R JV Pressure, Pout,RJV mmHg 3 [17,18]

L JV Pressure, Pout,LJV mmHg 3 [17,18]

Blood Viscosity, kg m-1 s-1 0.0035 [16]

CSF Ventricles Flow, fCSF,normal ml min-1 0.35 [5,6]

CSF Ventricles Flow, fCSF,CPP ml min-1 0.80 [21]

LV Diameter, Dshunt mm 3* [22]

4V Diameter, Dshunt mm 3* [22] * Estimated value based on current shunt systems available.

M. Strama et al. 7

Figure 4. Sensitivity analysis of microvasculature resistances in

order to obtain physiological accurate cerebral blood flows. 77.4%

reduction of the resistance in microvasculature will result in

physiological accepted cerebral blood flows.

Table 2 Cerebral Microvasculature Sensitivity Analysis on Cerebral Blood Flow

Flow Rates (ml min-1)

MVR R

ICA

L

ICA BA RJV LJV

Inflow

* Residual

90.0 280 227 796 651 651 1303 553 80.0 188 152 482 411 411 822 72

78.0 176 142 448 383 383 766 16

77.5 173 140 440 376 376 753 3

77.4 173 140 438 375 375 750 0

77.3 172 139 437 374 374 748 2

77.0 170 138 432 370 370 740 10 75.0 161 130 404 347 347 695 55

70.0 140 114 348 301 301 602 148

MVR = Degree of microvasculature reduction.

Gray rows represent omitted data from Figure 4. * Ideal cerebral blood inflow rate is 750 ml min-1 as determined from

[10,20].

2.5.2 Establishing CSF Flow

To accurately account for CSF production, the flows in the CP are set to a value of 350 l min-1. The resistances are

found by utilizing the representative lengths and diameters of each flow connection within the network. The assumption of

using these characteristic lengths takes into account that the flow networks in the brain are complex and non-linear resulting

in a scaling of lengths and diameters.

2.5.3 ICP Determination

The pressure in the model is not exactly ICP, but is directly related because since the ventricles do not expand, the

pressure created in the CSF system is the driving force. A rough estimate of the ICP will be calculated by taking the average

of the pressures over the ventricles in the CSF system.

2.6 Model Simulations

Five simulations will be conducted as shown in Figure 5 (page 8) to retrieve flow rates and pressure values: (1) a normal

state with no CPP, (2) CPP induced in the LLV, (3) CPP induced in the 4V, (4) treatment of CPP induced in the LLV with

a shunt, and (5) treatment of CPP induced in the 4V with a shunt. The simulation for the normal state with no CPP serves

as the control. When CPP is simulated in the LLV and 4V the CSF production by the CP goes up from 350 l min-1 to 2.08

ml min-1 as shown in clinical case studies [21]. CSF production of 800 l min-1 was used because the value is double the

normal production value and falls comfortably in the range of observed CSF production values. Incorporating a shunt with

the increased CSF production rate during CPP growth will help determine effective treatments by examining the pressures

and flows.


1

2

3

4

5

Figure 5. Experimental model

simulations of choroid plexus

papilloma (CPP). The left column

represents the location where CPP

would grow in the actual human

brain. The right column reflects the

CPP growth in the human brain

with respect to the given model

being used. Simulation 1 will serve

as a control brain with no choroid

plexus papilloma (CPP).

Simulation 2 will be conducted

with CPP growing in the left lateral

ventricle (LLV) while simulation 3

will be conduction with CPP

growing in the fourth ventricle

(4V). Simulation 4 will include a

shunt during CPP growth in the L

LV. Simulation 5 will include a

shunt during CPP growth in the

4V.

M. Strama et al. 9

3. Results

While the microvasculature of the cerebral blood flow is modified, the CSF system will remain unaffected by these

modifications. CSF circulates independently of the cerebral blood flow and its secretion is governed by the CP. Thus, when

the CSF system is modified, the cerebral vasculature system remains unaffected. The latter justifies why making the flow a

constant value of 350 l min-1 for normal CSF production will not impact the flows through the rest of the network.

3.1 ICP Profiles

Figure 6 (page 10) shows the ICP pressure profiles obtained for the control brain with no CPP, the experimental brains

with CPP, and the experimental brains with CPP in the presence of the shunt treatment from the model. The overall flow

profiles remain relatively unchanged and are omitted while the ventricular pressure profiles show a significant change

between the simulation conditions. With CPP, the pressures in the brain increase in magnitude and frequency compared to

the brain without CPP and decrease when a shunt is applied.

Table 3 analyzes the ventricular pressure profiles between the conditions by showing the ICP pressure for each

ventricular pressure profile. In the normal brain, the model estimated an ICP value of 13.15 mmHg which falls into the

normal range of ICP values for a healthy brain without external conditions. In the CPP inflicted brain, the model estimated

an ICP value of 20.53 mmHg which falls above the normal range of ICP values. When the shunt treatment is applied to the

CPP growth area in the LLV, the ICP value falls from the unhealthy value of 20.53 mmHg to a relatively normal value of

15.75 mmHg and to 14.13 mmHg when the shunt is applied to the CPP growth area in the 4V.

3.2 Conservation of CSF Flow

The preliminary results of the model suggest that the simulations may physiologically model actual cerebral

hemodynamics and onset stages of CPP based on overviews of the cerebral vasculature system and CSF system. Further

analysis of the CSF system is undertaken to acquire more insight of CSF dynamics.

Figure 7 shows the simulation data of the CSF dynamics through the CSF system in the control brain. The simulation

conveys that CSF flow is conserved when it transverses the ventricular network. The CSF into the ventricular network

equals the CSF leaving the ventricular network. Furthermore, CSF does not travel in a uniform fashion but is distributed

into various quantities as it transverses the ventricular network as shown in Table 4. The latter will be an important insight

into analyzing the CSF system in the presence of CPP and in the presence of CPP with a shunt. No matter the situation,

conservation of the CSF must be maintained. Even though the CSF inflow rates have increased due to CPP cell

accumulation, the CSF is still distributed based on the ventricular resistances of the network with the CSF inflow equaling

the CSF inflow. These findings help validate that the model conserves flows not only in the cerebral vasculature system as

shown by the sensitivity analysis in Figure 4, but also in the CSF system even though these two systems are independent of

each other.

Figure 7. CSF flow distribution

through the ventricular network of the

control brain. Conservation of CSF

flow holds since the CSF inflow

shown in A equals the CSF outflow

shown in B as CSF transverses the

ventricular network through various

pathways.

A

B

Table 3 ICP Pressure Simulation Estimate Results

Brain Condition ICP

(mmHg)

Control 13.15

With CPP* 20.53

With CPP and Shunt in L LV 15.75

With CPP and Shunt in 4V 14.13

* CPP condition is simulated as an increase in CSF flow rate from 350 l

min-1 to 800 l min-1 due to the accumulation of CPP cells, not CPP

growth.

Table 4 Normal Brain CSF System

CSF Inflow Rates

(ml min-1)

CSF Outflow Rates

(ml min-1)

L LV 0.1750 4 V L LV 0.1276

R LV 0.1233

R LV 0.1750 AV 0.0991

Total* 0.3500 Total † 0.3500

* Sum of L LV and R LV CSF inflows. Sum of L LV and R LV CSF outflows.

† Sum of 4V and AV CSF outflows.


A

B

C

D

E

Figure 6. Preliminary ICP results from the model simulations. Graph A displays the ICP normal probability density distributions

from each simulation obtained from graphs B-E. The distributions are overlapped to compare the conditions against each other. The

control distribution contains high probabilities of lower pressures. The CPP distribution contains high probabilities of high pressures

compared to the control. The treatments each reduce the probability of high pressures. Graph B shows the ventricular pressures for

the control simulation, Graph B for the brain with CPP simulation (for LLV and 4V), Graph C for the brain in the presence of CPP

in the LLV with shunt treatment, and Graph D for the brain in the presence of CPP in the 4V with shunt treatment. The frequency of

the magnitudes of the ventricular pressures change depending on the condition of the brain. When the shunt treatment is applied, the

frequency of the magnitudes of the ventricular pressures decrease in order to stabilize the ICP down to normal conditions.

M. Strama et al. 11

3.3 Simulation Results

Since the preliminary data validates that the model conserves flows in both the cerebral vasculature system as well as

the CSF system, further investigation into the CSF system may be explored. As described previously, the CPP growth will

be analyzed in the LLV and the 4V along with shunt treatments in each respective CPP growth area.

3.3.1 ICP Dynamics

Figure 8 (page 12) displays the ICP pressures in the CSF system in response to each simulation condition. When CPP

grows in the LLV and the 4V, the ICP increases. When the shunt is applied to the area of CPP growth, the ICP decreases to

values around the normal ICP range for humans (7-15 mmHg). These results give insight that shunt treatments may be

effective in stabilizing the CSF system in the presence of CPP growth. To gain further insight into the effectiveness of

shunts during CPP growth, analysis of the CSF flows for each condition must be undertaken.

Table 5 Left Lateral Ventricle CPP Growth without Shunt Treatment

CSF Outflow Rates (ml min-1)

CPP

Growth (%)

ICP

(mmHg) LLV RLV AV 4 V

0* 20.53 0.2917 0.2817 0.2265 0.5735 1 20.60 0.2907 0.2817 0.2276 0.5724

10 21.39 0.2788 0.2818 0.2393 0.5606 20 22.73 0.2588 0.2819 0.2593 0.5407

30 24.79 0.2280 0.2821 0.2899 0.5101

40 27.79 0.1831 0.2824 0.3345 0.4655

50 31.65 0.1255 0.2827 0.3918 0.4082

60 35.57 0.0669 0.2831 0.4500 0.3500

70 38.39 0.0247 0.2833 0.4920 0.3080 80 39.69 0.0052 0.2834 0.5114 0.2886

90 40.02 0.0003 0.2838 0.5162 0.2838

100 † 40.04 ~ 0 0.2835 0.5165 0.2835

Sum of L LV and R LV CSF outflows.

* Simulation includes increased CSF production rate at the very start as a result of CPP tumor cell accumulation.

† When CPP completely blocks the LV, system becomes unstable and fails;

as a result, 99.99% is used as the upper limit.

Table 6 Left Lateral Ventricle CPP Growth with Shunt Treatment


CPP

Growth (%)

ICP

(mmHg) LLV RLV AV 4 V Shunt

0* 15.75 0.3329 0.2853 0.1672 0.0476 0.6893

1 15.76 0.3206 0.2852 0.1672 0.0353 0.6770

10 15.82 0.2230 0.2847 0.1678 0.0617 0.5794

20 15.88 0.1414 0.2842 0.1682 0.1429 0.4978

30 15.91 0.0837 0.2839 0.1686 0.2001 0.4402

40 15.94 0.0455 0.2837 0.1688 0.2382 0.4019

50 15.95 0.0220 0.2835 0.1689 0.2615 0.3785

60 15.96 0.0090 0.2835 0.1690 0.2744 0.3655

70 15.97 0.0029 0.2834 0.1690 0.2806 0.3593

80 15.97 0.0006 0.2834 0.1690 0.2828 0.3570

90 15.97 ~ 0 0.2834 0.1690 0.2834 0.3565

100 † 15.97 ~ 0 0.2834 0.1690 0.2834 0.3564


* Simulation includes increased CSF production rate at the very start as a result of CPP tumor cell accumulation. Flow has reversed direction.

† When CPP completely blocks the LV, system becomes unstable and fails; as

a result, 99.99% is used as the upper limit.

Table 7 Fourth Ventricle CPP Growth without Shunt Treatment


CPP Growth

(%)

ICP

(mmHg) LLV RLV AV 4 V

0* 20.53 0.2917 0.2817 0.2265 0.5735

1 20.54 0.2917 0.2817 0.2266 0.5734

10 20.62 0.2913 0.2813 0.2273 0.5727 20 20.76 0.2907 0.2806 0.2287 0.5713

30 21.04 0.2894 0.2793 0.2313 0.5687

40 21.60 0.2868 0.2766 0.2366 0.5634 50 22.86 0.2810 0.2705 0.2485 0.5515

60 26.12 0.2659 0.2548 0.2792 0.5208

70 35.46 0.2228 0.2099 0.3673 0.4327

80 58.46 0.1166 0.0991 0.5842 0.2157

90 79.14 0.0212 0.0004 0.7792 0.0208

100 † 81.34 0.0110 0.0110 0.8000 ~ 0

Sum of L LV and R LV CSF outflows. * Simulation includes increased CSF production

rate at the very start as a result of CPP tumor cell accumulation. Flow has reversed direction.

† When CPP completely blocks the 4V, system becomes unstable

and fails; as a result, 99.99% is used as the upper limit.

Table 8 Fourth Ventricle CPP Growth with Shunt Treatment


CPP Growth

(%)

ICP

(mmHg) LLV RLV AV 4 V Shunt

0* 14.13 0.3199 0.3112 0.1689 19.5818 20.2129

1 14.12 0.3200 0.3112 0.1687 18.9121 19.5434

10 14.07 0.3206 0.3119 0.1675 13.4818 14.1143

20 14.02 0.3211 0.3124 0.1664 8.7254 9.3590

30 13.99 0.3215 0.3128 0.1656 5.2470 5.8814

40 13.97 0.3218 0.3131 0.1651 2.8808 3.5157

50 13.95 0.3220 0.3133 0.1647 1.4039 2.0391

60 13.94 0.3221 0.3134 0.1646 0.5784 1.2138

70 13.94 0.3221 0.3134 0.1645 0.1835 0.8190

80 13.94 0.3221 0.3134 0.1644 0.0363 0.6718

90 13.94 0.3221 0.3134 0.1644 0.0023 0.6378

100 † 13.94 0.3221 0.3134 0.1644 ~ 0 0.6356


* Simulation includes increased CSF production rate at the very start as a result of

CPP tumor cell accumulation. Flow has reversed direction.

† When CPP completely blocks the 4V, system becomes unstable and fails; as a

result, 99.99% is used as the upper limit.


A

B

C

D

E

Figure 8. ICP pressures in the CSF system in response to each simulation condition. Graph A overlays graphs B-E together to assess how each

condition compares to one another in changing the ICP. (The legend in graph A is universal for the other graphs.) ICP increases the most when

CPP grows in the 4V without shunt treatment compared to CPP growth in the LV without shunt treatment. Both conditions result in ICP values

way above the normal range of 7-15 mmHg. When the shunt is applied to each CPP growth area, the ICP values decline and hover around the

upper limit of the normal range of ICP values. These results give insight into the effectiveness of a shunt treatment for CPP.

M. Strama et al. 13

3.3.2 CPP in the LLV without Shunt

Figure 9 (page 14) provides quantitative results of the CSF system in the presence of CPP growth in the LLV. As the

CPP grows in the LLV, the ICP increases to accommodate the decrease in flow through the LLV. Since less CSF is flowing

through the LLV, the CSF flowing through the 4V decreases too. To compensate for this decrease, the CSF flow in the AV

increases. The RLV remains relatively unaffected. Table 5 displays that at any given percent reduction in diameter from

CPP growth, the sum of CSF in the 4V and in the AV equals the CSF inflow of 800 l min-1.

3.3.3 CPP in the LLV with Shunt

Figure 9 also provides quantitative results of the CSF system in the presence of CPP growth in the LV and in response

to the shunt treatment. As the CPP grows in the LLV, the ICP increases at a slower rate due to the presence of the shunt.

The CSF is being restricted from flowing through the LLV due to the LLV’s increasing resistance. The shunt exhibits lower

resistance, so CSF will flow down the shunt instead of down the LLV. Due to the shunt, the CSF system remains stable

with relatively no increase in AV CSF flow. Table 6 displays that the ICP values remain slightly above the normal range of

ICP values.

3.3.4 CPP in the 4V without Shunt

Figure 10 (page 15) provides quantitative results of the CSF system in the presence of CPP growth in the 4V. As the

CPP grows in the 4V, the ICP increases rapidly to accommodate the decrease in flow through the 4V. The 4V is essentially

the only exit for the CSF from the LLV and RLV. Since the 4V is increasing in resistance, the CSF will not flow through

it. Instead, the CSF will flow through the AV, which also contain high resistances. However, the AV has a lower total

resistance so the CSF will flow down these pathways to accommodate the blockage of the 4V by CPP. Since the RLV and

LLV drain into the 4V, CSF will similarly stop flowing through these pathways until all the CSF will flow through the AV.

As the AV in increasing in CSF flow, the ICP is drastically increasing to keep the CSF flowing through this relatively high

resistance pathways as shown in Table 7.

3.3.5 CPP in the 4V with Shunt

Figure 10 also provides quantitative results of the CSF system in the presence of CPP growth in the 4V and in response

to the shunt treatment. The shunt again helps stabilize the CSF system by keeping the CSF flow through the LLV, RLV,

and AV relatively constant. Due to this increased stability, the ICP decreases because the shunt effectively acts as the 4V

but with a lower resistance with reversal flows noted in Table 8.

3.3.6 CSF Flow Distribution Schematics

To further analyze the CSF flows through the CSF network, flow schematics for each simulation were constructed to

help visualize the CSF auto-regulation mechanisms as shown in Figure 11 (page 16).

4. Discussion

Once the microvasculature sensitivity analysis was performed and applied to the network, values obtained were close

to measured physiological values. For the control brain, the total cerebral vasculature blood inflow and outflow was 750.35

ml min-1, which compared well to the ideal cerebral vasculature volumetric blood flow rate of 750 ml min-1 [10, 20]. This

result validates the cerebral vasculature system model as accurate when accounting that the inflows need to equal the

outflows as can be seen in the Table 2 where the outflow though the RJV and LJV sum together to equal the sum of the

inflows from the RICA, LICA, and BA. The conservation holds for the CSF system as well. Furthermore, when the model

was applied to the CSF system, the simulation yielded an ICP of 13.15 mmHg, which falls comfortably in the ICP range for

a normal brain of 7-15 mmHg [19]. Since the validity of the model is established, the results obtained from the experimental

groups can be analyzed with more certainty.

When the brain is inflicted at early stages of CPP, the ICP increases to a value of 20.53 mmHg, which is above the

normal ICP range. Furthermore, when the shunt treatment is applied either the LLV or 4V, the ICP decreases down into

normal regions of 15.75 and 14.13 mmHg, respectively.


CPP in L LV without Shunt CPP in L LV with Shunt

L – R LV

4V

AV

SHUNT

Figure 9. (Left column) Left lateral ventricle choroid plexus

papilloma growth without shunt treatment flows. As the CPP

grows in the LLV, the LLV resistance increases and as a result,

the CSF flow becomes more restricted and decreases through the

LLV. To compensate for the CSF flow restriction through the

LLV, the ICP increases to drive the CSF into other ventricular

pathways such as the AV. (Right column) Left lateral ventricle

choroid plexus papilloma growth with shunt treatment flows. As

the CPP grows in the LLV, the LLV resistance increases and as a

result, the CSF flow becomes more restricted through the LLV.

Instead, the CSF flows down the shunt which has a lower

resistance. The shunt helps to keep the CSF system stable by not

increasing the CSF flow through the AV, and as a result, the ICP

values remain relatively unchanged.

M. Strama et al. 15

CPP in 4V without Shunt CPP in 4V with Shunt

L – R LV

4 V

AV

SHUNT

Figure 10. (Left column) Fourth ventricle choroid plexus

papilloma growth without shunt treatment flows. As a result of

the CPP growing in the 4V, a ‘bottleneck’ effect forms where CSF

buildups up and the flow through the LLV and RLV ceases. To

compensate for this ‘bottleneck’, the CSF flows down the AV.

The AV contain relatively high resistances, but their total

resistance is lower than the resistance in the 4V due to CPP

growth. Since CSF is flowing down the AV microstructure, the

ICP drastically increases in order to effectively drive the CSF.

(Right column) Fourth ventricle choroid plexus papilloma growth

with shunt treatment flows. The shunt stabilizes the CSF system

by allowing the LLV, RLV, and AV to remain relatively constant

CSF flows. The shunt acts as the 4V connecting pathway from the

LLV and RLV but with a lower resistance which in turn allows

the ICP to decrease.


Normal Brain

CPP in LLV without Shunt

CPP in LLV with Shunt

CPP in 4V without Shunt

CPP in 4V with Shunt

Figure 11. Representative CSF flow distribution

through the ventricular network for each

simulation performed. The normal brain CSF flow

distribution represents the baseline for the

comparison between the other four simulations.

The arrows in the schematic represent the relative

magnitude of the CSF flow through the region of

interest. The schematics illustrate the results

obtained in a visual manner to aid in

understanding the auto-regulation of the CSF

system in response to each given simulation. In

the normal brain, the CSF enters the LLV and

RLV at a rate of 400 l min-1. Some CSF is

distributed into the AV causing a decrease in CSF

flow rate towards the 3V for each LV. The LLV

and RLV combine at the fork and the CSF flow

increases down the 3V into the 4V. The CSF flow

distribution in the 4V is the sum of the LLV and

RLV minus the AV. This situation is identical to

that seen in figure 7 and table 4. When CPP is

present in the LLV, the CSF flow distribution into

the back end of the LLV decreases while the flow

into the AV increases. When CPP is present in the

4V, a ‘bottleneck’ effects occurs and the CSF flow

distribution is repelled in a reverse direction.

When the shunt is applied, these schematics help

illustrate how reverse flows occur as well as how

the AV become stabilized.

M. Strama et al. 17

When further analysis into the CSF system as CPP develops is explored along with the shunt treatment, reverse flows

occur. Flows are controlled by pressure gradients where positive flows are defined as a flow going from an area of high

pressure to an area of low pressure. The flow connections were predetermined based on the construction of the brain model.

Reverse flows are more prevalent in the shunt treatment systems due to the fact that the pressure at the outlet of the shunt is

set to zero. The pressure at the outlet is set to zero to take into account that the shunt length is not realistic in this model.

Shunt extend all the way down to the abdomen or heart given the type of shunt [22]. Thus in the conservation balance

equations, these reverse flows will be negative. An example is in Figure 17 where the shunt flow plus the AV flow minus

the reversal 4V flow equals the total CSF inflow of 800 l min-1.

When CPP grows in the LLV or in the 4V, the ICP grows uncontrollably. The ICP increases since one of the CSF flow

pathways is being occluded. The increase in ICP generates a driving force for the CSF to flow through the AV. The AV is

part of the SAS which contains high resistance so flow through these structures is low. The fact that the flow is increasing

through these structures highlights the CSF system’s auto-regulation ability to accommodate the increase in ICP. To have

more flow occurring in the AV causes the SAS structure to expand and will lead to major health problems or death [23].

When the shunt is applied to the LLV, the shunt is most effective after about 40% CPP growth. Under 40% CPP growth,

CSF flow through the 4V is limited while the AV and RLV flows are maintained. The ICP also begins to climax and settles

at a constant value with relatively no change. When the shunt is applied to the 4V, the shunt is effective from the very onset

of CPP growth. The LLV, RLV, and AV flows remain constant and the ICP decreases to a constant value. The reason why

the shunt is immediately effective is due to the ‘bottleneck’ effect that the CPP creates in the 4V.

5. Conclusion

As a result of this simulation, the CSF flow patterns inside the ventricular and subarachnoidal regions during CPP

growth were analyzed as well as the auto-regulation of the CSF system during treatment of CPP via insertion of a shunt. By

reducing the diameter of the area affected in the CSF system due to CPP growth, the details of how the CSF flows respond

became clear. ICP increases with increasing CPP growth until a point where human health is severely deteriorated by the

flow distribution within the CSF system as a result of the CSF auto-regulation mechanisms.

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