View of Physiology 11 2.1 Thecardiovascularsystem

MATHEMATICAL MODEL FOR HEMODYNAMIC AND INTRACRANIAL WINDKESSEL MECHANISM

THUNYASETH SETHAPUT

Submitted in partial fulﬁllment of the requirements For the degree of Doctor of Philosophy

Dissertation Advisor: Dr. Kenneth A. Loparo

Department of Electrical Engineering & Computer Science

CASE WESTERN RESERVE UNIVERSITY

May 2013 CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

John James Doe ______Thunyaseth Sethaput

Doctor of Philosophy candidate for the ______degreeDoctor of Philosophy *.

Committee Chair (signed)______Kenneth A. Loparo (chair of the committee)

Committee Member ______Vira Chankong

Committee Member ______Mark Buchner

Committee Member ______Evren Gurkan-Cavusoglu

Committee Member ______

Date of Defense (date) ______07 December 2012

*We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents

TableofContents...... iii ListofTables ...... v ListofFigures...... vi Acknowledgement...... xvi Abstract...... xviii

1 Introduction 1 1.1 MotivationandLiteratureSurvey ...... 1 1.2 Contributions ...... 6 1.3 OutlineoftheDissertation ...... 8

2 Review of Physiology 11 2.1 TheCardiovascularSystem ...... 11 2.1.1 Heart ...... 12 2.1.2 VascularSystem ...... 12 2.2 IntracranialSpace...... 21 2.2.1 Brain...... 21 2.2.2 CSFandVentricularSystem...... 23 2.2.3 CerebralBloodFlow ...... 25 2.3 PathologicalConditions ...... 27 2.3.1 Stroke ...... 27 2.3.2 TraumaticBrainInjury...... 29 2.3.3 Hydrocephalus ...... 32

3 Associated Intracranial System 38 3.1 Windkessel Mechanism and Pulsatility ...... 39 3.2 Monro-KellieDoctrine ...... 44 3.3 IntracranialCompliance ...... 47 3.4 InterhemisphericPressureGradients ...... 57 3.5 Eﬀect of Neurosurgical Disorders on Cerebral Blood Flow ...... 64

iii 4 Review of Windkessel Model and the Model of Intracranial System 72 4.1 ReviewofWindkesselModel...... 72 4.2 ReviewoftheModelofIntracranialSystem ...... 76

5 Mathematical Model 90 5.1 ContinuityEquation ...... 91 5.2 The Equation for the Acceleration of the Elastic Blood Vessel . . . . 92 5.3 Hagen-Poiseuille’sLaw ...... 93 5.4 The Relationship of Flow and Pressure in Oriﬁce ...... 94 5.5 BloodFlowthroughCranium ...... 95 5.6 Pressure-VolumeRelationship ...... 97 5.7 InterhemisphericPressureGradients...... 98 5.8 Interhemispheric Asymmetry of Cerebral Blood Flow ...... 99 5.9 The Case of Neurosurgical Disorder ...... 100 5.10 The Case of Treatment by using a Medical Balloon ...... 101

6 Simulation Results 103 6.1 NormalCondition...... 103 6.1.1 LowerBody ...... 104 6.1.2 UpperBodyandIntracranialSpace ...... 104 6.2 CaseofNeurosurgicalDisorder ...... 112 6.2.1 Smallmasslesion ...... 113 6.2.2 Largemasslesion ...... 115 6.3 Case of Treatmentbyusinga MedicalBalloon ...... 120 6.3.1 Smallmasslesion ...... 120 6.3.2 Largemasslesion ...... 124 6.4 Discussion...... 127

7 Summary and Conclusions 134 7.1 Summary ...... 134 7.2 RecommendationsforFuture Development ...... 136

A Parameters for the Model of Hemodynamics and Intracranial Sys- tem 137

iv List of Tables

2.1 Characteristics of various types of blood vessels in humans [10]. . . . 14

3.1 Summary of types of lesion according to CT scan and ICP pattern [144]. 62 3.2 Effect of extradural expanding lesion on cerebral blood flow [163]. . . 68 3.3 Regional and total brain cerebral blood flow in rats subjected to fluid- percussionbraininjury[197]...... 69

4.1 Summary of the equivalent between pulsation of CSF and oscillations of electricityin an AC electricalcircuit[46] ...... 83

6.1 Comparison table of ICP, cerebral blood flow (Qbrain) and flow to hands (Qhand) during normal condition, with small mass lesion and afterinversiontreatment ...... 123 6.2 Comparison table of ICP, cerebral blood flow (Qbrain) and flow to hands (Qhand) during normal condition, with large mass lesion, and afterinversiontreatment ...... 126

A.1 Parameters for the Model of Hemodynamics and Intracranial System 137 A.1 Parameters for the Model of Hemodynamics and Intracranial System 138 A.1 Parameters for the Model of Hemodynamics and Intracranial System 139

v List of Figures

1.1 Current and projected numbers of patients with hydrocephalus, aged 18 to 35, treated in the United States. Dark bars indicate projections of numbers of patients based on the actual numbers treated at Intermountain Healthcare; lighter bars indicate future projections for young adults with hydrocephalus. Data source from Intermountain Healthcare[154]...... 2

2.1 Pulsatile blood flow in the root of the aorta recorded using an electro- magneticflowmeter[69]...... 13 2.2 Blood pressure in different segments of the vascular system[78]. . . . 14 2.3 Movement of blood into and out of the arteries during the cardiac cycle. The lengths of the arrows denote relative quantities flowing into and out of the arteries and remaining in the arteries [193]...... 16 2.4 Changes in the pulse pressure contour as the pulse wave travels toward thesmallervessels[69]...... 17 2.5 The major arteries that carry blood from the left ventricle of the heart tothetissuesofthebody[148]...... 20 2.6 (a) The surface of the cerebral cortex and the divisions of the brain shown in sagittal section [193], (b) Investing membranes of the brain, showing their relation to the skull and to brain tissue [10]...... 22 2.7 (a) The pathway CSF flow from the choroid plexus in the lateral ventricles to arachnoid villi penetrating into sagittal sinus [69]. (b) Ven- tricularsystemofthebrain[173] ...... 24 2.8 The internal carotid artery and vertebro-basilar system. Note the cerebral arterial circle (circle of Willis; marked by a dashed black line) [152]. 26 2.9 Axial noncontrast CT demonstrates an epidural hematoma [199]. . . 30 2.10 (a) Axial view of a subdural hematoma [110]. (b) Computed tomography indicated a large right-sided acute on chronic subdural hematoma (maximum depth, 1.9 cm) occupying the frontal, parietal and temporal convexities, and a possible small subarachnoid hemorrhage [196]. . . . 32

vi 2.11 T1 weighted axial and sagittal magnetic resonance images of the brain in patients with ((b) and (d)) and without ((a) and (c)) hydrocephalus. The ventricles are markedly enlarged compared to normal. The cerebral aqueduct (arrow) is patent and there is no evidence of obstruction within the ventricular system. This is a case of communicating hydrocephalus[28]...... 34 2.12 Cerebral blood flow in (a) healthy individuals and in (b) communicating hydrocephalus. (a) The arterial windkessel mechanism, the wide intracranial vessels with small vascular resistance and the venous outflow resistance that keep the cerebral veins distended maintain the high normal blood flow. The venous outflow resistance is caused by a small positive intracranial pressure and is increased during systole. The venous outflow resistance is a mandatory prerequisite for the “waterfall phenomenon”, i.e. the pressure drop occurring from the cortical veins to the venous sinus. (b) In communicating hydrocephalus, the increased transmantle pulsatile stress (i.e. difference in pressure between ventricle and subarachnoid space) and the ventricular dilation compresses the cerebral veins and capillaries in their entire length. This significantly increases the vascular resistance and decreases the blood flow. The reduced venous outflow resistance facilitates collapse of the compressed capacitance vessels, which further decreases cerebral blood flow[66]...... 35 2.13 (a) Preoperative MRI of a 7-year-old boy with monoventricular hydrocephalus due to shunt overdrainage: marked dilatation of the left lateral ventricle (b) MRI performed 10 days after the endoscopic fenestration of the septum pellucidum: marked decrease of size of the left lateral ventricle and reappearance of the subarachnoid spaces [55]. . . 36

3.1 The concept of Windkessel mechanism. The air reservoir (chamber) is the actual Windkessel, and the large arteries act as the Windkessel. The combination of compliance, together with aortic valves and peripheral resistance, results in a rather constant peripheral ﬂow [189] . 39 3.2 Pressure-dependent arterial compliance [103] ...... 40

vii 3.3 Central pressure contours and aging. The observed central pressure contours (upper tracings) are the sum (lower tracings) of the incident or forward-traveling wave (broken lines) and the reflected or backward- traveling wave (dotted lines). In younger subjects (right panel), the reflected wave (arrow) returns to the aortic root during diastole. As vessels get stiffer during the aging process (left panel), pulse wave velocity increases and the reflected wave returns during late systole (arrow), where it summates with the forward systolic wave to augment central systolic pressure and increase ventricular afterload [77]. (Adapted from AsmarR.ArterialStiffness. 1999. [4]) ...... 42 3.4 Diagram showing the phase relationships of intracranial volume change measured by using flow-sensitive MRI in (a) normal individuals and (b) patients with hydrocephalus. The curve of the volume changes in the artery is constructed as the inverse to the sum of the changes in the veins and intracranial CSF. In normal individuals, the expansion in the precapillary vessels is assumed to be somewhat larger than the corresponding compression on the venous side in order to correspond with the small brain expansion. In patients with hydrocephalus, the arterial is small as reflected in the small volume changes in the veins and in the intracranial CSF. As a result of the small arterial pulsations in SAS the pulse wave penetrates into compliant less distended intracerebral vessels resulting in a decreased intrinsic redistribution and large brain expansion[61]...... 45 3.5 Normal intracranial hydrodynamics. The relative thickness of the arrows in the artery (red) indicates the magnitude of pressure. The relative thickness of the arrows in the venous system (blue) and subarachnoid space indicates the magnitude of flow [162]. (Modified from Greitz[66]) ...... 47 3.6 Illustration of the ICP-volume curve and its relationship to the intracranial pulsatility parameters. Under normal physiological conditions with high intracranial compliance, the ICP wave amplitude is correspondingly small. As intracranial compliance decreases (steep part of the pressure-volume curve), the brain behaves increasingly like a linear elastance and so variations in intracranial volume correlate increasingly well with changes in mean ICP, the steepness of the pressure-volume curve also accounts for large-amplitude ICP waveforms [48]...... 48 3.7 (a) The CSF volume-pressure curve (b) The same data plotted on semilogarithmic axis can be approximated by a straight line which its slope is equal to the pressure-volume index (PVI) [113]...... 49

viii 3.8 Schematic depiction of the pressure-volume compensation index (RAP) theory[83]...... 51 3.9 Timetrends of intracranial pressure (ICP), arterial blood pressure (ABP), cerebral perfusion pressure (CPP), mean cerebral blood flow velocity (FVm), pulsatility index (PI) and cerebrovascular resistance (CVR) in patientwithhead-injury[44]...... 53 3.10 (a) Arterial and venous flow in the superior sigital sinus (SSS) territory in a healthy patient. (b) In NPH patient, arterial and venous flows are almost identical shape with minimal delay. The mean volumetric blood flow through SSS in NPH patients is 27% lower than in the healthy individuals. (c) After shunting (removal of 30 mL of CSF), the arterial flow has earlier, higher, and thinner peak. The venous flow peaks later, islower,and wider. Modifiedfrom Bateman[11]...... 55 3.11 Mean values of epidural pressure on the right (PR) and left (PL) sides in various groups of animals. Oil embolization always performed on the right side. All pressures are positive. The animals in which epidural pressure increase was more pronounced on the right (embolized) side were inscribed above the x-axis. The animals which epidural pressure increase was more pronounced on the left (non-embolized) side were inscribed below x-axis. Interhemispheric pressure gradients were more pronounced when epidural pressure increased more on the non- embolized(left)side.[20]...... 59 3.12 Injection of Pantopaque into right middle cerebral artery of cat [167] 60 3.13 Alternating inflation of two balloons over left and right hemisphere of baboon[167]...... 61 3.14 Difference between ipsilateral and contralateral ICP recording from patients with (a) subdural hematoma and (b) contusions or intracerebral hematoma[27]...... 62 3.15 Interhemispheric ICP gradients and infarct volumes for all animals. Hourly interhemispheric ICP gradients (mmHg) are plotted over time. Percent ipsilateral hemispheric infarct volume is noted for each animal [39]...... 63 3.16 Effect of acute expansion of the extradural balloon on carotid blood flow (BF), jugular vein pressure (Jug), intracranial pressure (ICP), sagittal sinus pressure (Sag), lumbar subarachnoid pressure (Lum) and systemic arterial pressure (SAP). Arrow indicate beginning and end of injection. Time between triangles one minute. In this and all subsequent illustrations pressures are indicated in mmHg and flow in ml/min.[93]...... 66

ix 3.17 Mean right and left cerebral hemisphere blood flow levels, with increasing meanintraventricularpressure[79]...... 67 3.18 Changes in regional cerebral blood flow (rCBF) in the visual (A), parietal (B), sensorimotor (C), and frontal cortices (D) of the injured and the contralateral sides. rCBF decreased remarkably in the injured side following insult for 4 hours. After 24 hours, rCBF recovered except in the visual cortex. rCBF also decreased slightly in the non-injured side. Modified from Ozawa et al. [135]...... 70 3.19 Graph showing ipsilateral and contralateral regional cerebral blood flow (CBF) values in measured areas in patients with intracranial hematomas. Regional CBF in parietal and temporal lobes was significantly lower on the side ipsilateral to the hematoma. Error bars indicate standard error of the mean. FR = frontal lobes; PA = parietal lobes; TE = temporal lobes; OCC = occipital lobes; BASG = basal ganglia; CBL = cerebellum; BS = brain stem [19]...... 71

4.1 (a) Two-element Windkessel model, (b) Three-element Windkessel model and (c) Four-element Windkessel model presented in hydraulic and electricalcircuits[189]...... 73 4.2 The measured aortic input impedance and impedance predicted by two-element,three-element and four-element Windkessel [189]. . . . . 75 4.3 Top: schematics of 3- and 4-element Windkessel (WK) models presented in electrical form. Rc and Rp, characteristic and peripheral resistance; C, total arterial compliance; L, inertance. Middle: aortic ﬂow measured in dog. Bottom: measured and model derived aortic pressure[161]...... 76 4.4 Lumped-parameter seven compartmental model of the cerebrovascular system. [ ] represents pressure in mmHg, ( ) represents ﬂow in ml/min., and <> representsvolumeinml[80]...... 77 4.5 Hydrodynamic equivalent of the model, comprising pathways of CBF and the CSF circulation.A rigid skull is represented by the outer box, with a compensatory reserve Ci associated with the compliant dural sac within the lumbar channel [35]...... 79 4.6 Electrical circuit equivalent to the hydrodynamic model[35]...... 79

x 4.7 Electric analog (A) and corresponding mechanical analog (B) of intracranial dynamics according to present model. Cerebral blood flow (CBF,q) enters skull at pressure approximately equal to systemic arterial pressure (Pa). Arterial-arteriolar cerebrovascular bed consists of a regulated capacity (Ca), which stores a certain amount of blood volume, and a regulated resistance (Ra), which accounts for pressure drop to capillary pressure (Pc). At capillary level, cerebrospinal fluid (CSF) is produced through a CSF formation resistance (Rf ). CBF then passes through venous cerebrovascular bed, mimicked as series arrangement of proximal venous resistance (Rpv) and resistance of collapsing lateral lacunae and bridge veins (Rdv). Model assumes that, because of collapse of last section, cerebral venous pressure (Pv) is always approximately equal to intracranial pressure (Pic). Finally, CSF is reabsorbed at venous sinus pressure (Pvs) through CSF outflow resistance (Ro). Intracranial pressure is determined by amount of volume stored in nonlinear intracranial compliance (Cic). This volume results from a balance between CSF inflow (qf ), CSF outflow (qo), blood volume changes in arterial capacity, and mock CSF injection rate (Ii). ModifiedfromUrsinoandLodi[171]...... 80 4.8 The 16 compartment whole-body model. A filled arrow indicates a one- way flow and a hollow arrow indicates a pressure dependent resistance. Compartment labels are enclosed in parentheses with the spatially- averaged mean pressures in square brackets. The thick line indicates thecranialwall[89]...... 82 4.9 (a) A model of CSF pulsation with a single degree of freedom.The CSF pulsation, which is the mass of CSF (mCSF ) displaced by the maximum expansion of the vessel is represented by sphere. The instantaneous displacement of the CSF pulsation is represented by xCSF (t). The external force of the vascular pulsation is assumed to be sinusoidal, and given by F0 sin ωt. The other forces acting on the pulsating CSF include a resistance force Rx˙ CSF (t) and an elastic force kE xCSF (t), representing the elasticity of the walls of the space. The net force acting on the CSF pulsation is the inertial force mCSF x¨CSF (t). (b) Equivalent RLC electrical circuit for CSF pulsation. Modified from Egnor et al. [46]...... 83

xi 4.10 (a) The intracranial Windkessel effect, which is the dissipation of arterial pulsations into the CSF, can be modeled by representing the intracranial blood and CSF as two separate masses connected by springs representing the elastic elements of vasculature and craniospinal contents. (b) The electical analog to a mechanical absorber is a wave trap, which is main RLC circuit representing the capillary blood and a smaller parallel RLC circuit representing the CSF. Modified from Egnor et al. [46]...... 84 4.11 The intracranial filter circuit and the windkessel mechanism. Intracra- nial blood vessels and CSF spaces are arranged as parallel pathways branching from a series flow. Normal intracranial blood flow and CSF dynamics can be represented by a series-parallel array of blood vessels and CSF spaces. Modified from Egnor et al. [47]...... 85 4.12 (a) Schematic of CSF pathways, the vascular system and brain parenchyma. (b) The discretized model of CSF flow induced by choroid expansion a(t). Modified from Linninger et al. [101]...... 86 4.13 The Linninger et al.’s multi-compartment model with one arterial pressure in the carotid Pinit as input signal and the venous pressure in the jugular vein is Pout. Modified from Linninger et al. [102]...... 88

5.1 The initial pulse cardiac output, generated by heart, is the combination of three sets of sinusoidal wave with random heart rate...... 91 5.2 (a) Cross-sectional area of blood vessel (b) Elastic blood vessel (c) Free body diagram of blood with pressure and elastic forces exerting on . . 92 5.3 Hagen-Poiseuille’s law represent the blood flow resistance caused by the length of artery in term of the pressure drop between inflow and outflow...... 93 5.4 The relationship of flow and pressure in orifice represented the peripheral resistance of blood flow due to the change of lumen size...... 94 5.5 (a) There are three forces exerting arterial and venous blood. (b) Blood flow through artery, capillaries and vein in the enclosed cranium space. (c) There are only two forces exerting on capillary blood...... 96 5.6 Combination of blood vessel’s stiffness (kart and kvein) and stiffness of elastic intracranial contents (kCSF ) in series result in less equivalent stiffness (keq) or more intracranial compliance of the CSF system . . . 97 5.7 (a) Intracranial space is divided into left and right hemispheres with midline displacement to describe the transmission of pressure and volume between left and right cerebral hemispheres. (b) Free body dia- gramofmidlinedisplacement...... 98 5.8 Blood flow to hand and cranium after passing ascending aorta . . . . 101

xii 5.9 Three different balloon cycle including augmentation, reduction and inversion used to increase cerebral blood flow. Modified from laboratory researchdataatClevelandclinic...... 102

6.1 Arterial blood flow through major arteries to lower limbs. Cardiac output (dark-blue), generated by heart, flow into ascending aorta and flow out at aortic arch (green). Then, blood flow into descending aorta to common iliac artery (orange), pass through external iliac artery (blue)andfemoralartery(purple)...... 105 6.2 Pressure and velocity pulse waveforms in the aorta and arterial branches of a dog. Note that the pressure maximum becomes amplified while the velocity maximum decreases as the blood moves downstream [26] 106 6.3 Ascending aortic blood pressure and flow waveforms...... 107 6.4 Common iliac arterial blood pressure and flow waveforms...... 107 6.5 Blood, after passing ascending aorta, flows into intracranial artery (dark blue) and capillaries (green) then flows into intracranial vein (red). Blood exits the intracranial space via intracranial vein repre- sentedbybluewaveform...... 108 6.6 Arterial (dark blue), capillary (green), and venous (red) blood pressure intheintracranialspace...... 109 6.7 Plot of vertebral artery pulsatile change in cerebral blood volume (CBV) and ventricular fluid pressure (VFP) during five cardiac cycles in dog. Note also the synchronization of the extreme values of the change in CBVandCSFpulse[6]...... 109 6.8 The phase relationship of predicted blood flow and pressure waveform in the intracranial space show that intracranial pressure (ICP), cerebral blood volume (CBV), intracranial arterial blood pressure (ABP) and arterial blood outflow (dark blue) are in-phase which delay from arterial blood inflow (black). ICP and ABP are in mmHg. CBV is in ml. Arterial blood inflow and outflow are in ml/sec. This figure is in agreement with Avezaat et al.’sMRI data [6](Figure6.7)...... 110 6.9 The expansion of intracranial arteries (∆xart) result in venous contraction (∆xvein) and intracranial volume reduction (Vol.) synchronously. Also, the delay of capillary expansion (∆xcap) after arterial expansion. This simulation results agree with Monro-Kellie doctrine and the diagram of phase relationship of blood and CSF from Greitz [61]’s MRI data(Figure3.4)...... 110

xiii 6.10 Upper: the timing relationship between arterial blood pressure (ABP) at femoral artery and ICP signal are observed in canine’s experimentation conducted by Cleveland clinic researchers. Lower: the small delay of ABP and ICP signal are predicted from the mathematical model based on human physiology which are in agreement with canine’smonitoring...... 111 6.11 After small mass lesion placing in right cerebral hemisphere, left hemisphere (dark blue) has higher ICP than right hemisphere (green). Dash black waveform represents ICP in normal condition (without mass lesion)...... 113 6.12 After small mass lesion placing in right cerebral hemisphere, positive displacement of midline refers to midline shift to right hemisphere whichhaslowerICP...... 114 6.13 After small mass lesion placing in right cerebral hemisphere, cerebral blood flow to the right hemisphere (thick green) becomes greatly lower. Also, the high pulsatility with shorter delay of right cerebral blood outflow (thin green) after systolic peak of arterial inflow is observed. However, no significant change of blood inflow (thick dark blue) and outflow waveform (thin dark blue) over left hemisphere is observed. . 115 6.14 After small mass lesion placing in right cerebral hemisphere, systolic expansion of artery in lesion hemisphere (green) becomes significantly lower compared to non-lesion side (dark blue)...... 116 6.15 After large mass lesion placing in right cerebral hemisphere, left hemisphere (dark blue) has lower ICP than right hemisphere (green). The dampened ICP waveform over lesion hemisphere is also observed. . . 117 6.16 After large mass lesion placing in right cerebral hemisphere, negative displacement of midline represent the displacement of midline forward tolefthemispherewhichhaslowerICP...... 117 6.17 After large mass lesion placing in right cerebral hemisphere, cerebral blood flow to both hemisphere becomes lower. Especially, on the lesion side, blood flow to the right hemisphere (thick green) ceases after 5 seconds...... 118 6.18 After large mass lesion placing in right cerebral hemisphere, arterial expansion of artery in lesion hemisphere (green) is severely restricted and becomes lower than the expansion of artery in contralateral hemisphere(darkblue)...... 119 6.19 After large mass lesion placing in right cerebral hemisphere, capillary in both hemisphere becomes more restriction compared to normal condition (dash black). Especially, the marked restriction of capillary in lesionhemisphere(green)isobserved...... 119

xiv 6.20 Inversion (blue) should do synchronously with cardiac output (thick red) to obtain most cerebral blood flow improvement. ICP response in left (dark blue) and right (green) cerebral hemisphere along inversion cyclearealsoplotted...... 120 6.21 Intracranial pressure in left (dark blue) and right (green) hemisphere withsmallmasslesion ...... 121 6.22 Intracranial pressure in left (dark blue) and right (green) hemisphere afterinversiontreatment ...... 121 6.23 Cerebral blood flow to the left (thick dark blue) and right (thick green) hemispherewithsmallmasslesion ...... 122 6.24 Cerebral blood flow to the left (thick dark blue) and right (thick green) hemisphereafterinversiontreatment ...... 122 6.25 Expansion of left cerebral artery (dark blue) and right (green) cerebral arterywithsmallmasslesion ...... 122 6.26 Expansion of left cerebral artery (dark blue) and right (green) cerebral arteryafterinversiontreatment ...... 122 6.27 Inversion (blue) should do nearly synchronously with cardiac output (thick red) to obtain most cerebral blood flow improvement. ICP response in left (dark blue) and right (green) cerebral hemisphere along inversioncyclearealsoplotted...... 124 6.28 Intracranial pressure in left (dark blue) and right (green) hemisphere withlargemasslesion ...... 125 6.29 Intracranial pressure in left (dark blue) and right (green) hemisphere afterinversiontreatment ...... 125 6.30 Cerebral blood flow to the left (thick dark blue) and right (thick green) hemispherewithlargemasslesion ...... 126 6.31 Cerebral blood flow to the left (thick dark blue) and right (thick green) hemisphereafterinversiontreatment ...... 126 6.32 Developmentalcycleof hydrocephalus...... 130

xv ACKNOWLEDGEMENTS

Before I can fulfill the requirements for Ph.D in the School of Engineering at Case Western Reserve University, I have experienced a long critical passage of my life. I left a hot and humid city of Bangkok for a cold and snowy city of Cleveland by myself. I turned from familiar field of mechanical engineering to no background knowledge of systems engineering. I have faced various kinds of challenges and hindrances to test my patience as well as my self-discipline. As years go by, these obstacles strengthen and enhance my subsistence. I have not only gained tremendous knowledge from the Faculty, but also many experience that provide me the understanding of life. However, without their constant help and encouragement from the following persons, my academic pursuits cannot be possible. First of all, I am profoundly grateful to Professor Kenneth A. Loparo, my research advisor who introduced biomedical system and modeling to me. He has persuasively provided the guidelines for my research methodology, critical thinking and problem solving. Without his invaluable guidance, my potentiality as researcher will not be kindled. He is really my role model of academic career. I am impressive with his academic devotion. His researching concept will be imprinted on my mind and my academic life. My heartily gratitude goes to Professor Vira Chankong, my academic and research co-advisor for his continuous academic and personal supports since I first came to the University. He gave me more opportunities for my study here in addition to introduce me to Professor Loparo and my challenging research topic. I always remember his care and warmth as same as my family members. I would like to extend my thanks to Dr. Mark Luciano, Dr. Stephen Dombrowski and Cleveland Clinic researcher who provided experimental data. They shared useful experiences of intracranial system and gave valuable comments and reflections. This research was supported in part by the National Institute of Health, grant R01

xvi NS060916. My sincere thanks also give to Professor Mark Buchner and Professor Evren Gurkan-Cavusoglu, my thesis defense examination committee. Their comments are very useful for me to improve my dissertation. My friends in Cleveland are “the friends indeed”, though I cannot mention all names. I certainly say a big thanks to Assistant Professor Adirak Kanchanaharuthai, Dr. Arsit Boonyaprapasorn and Wanchat Theeranaew. They are the part and parcel along the way of my success stories. They have rendered helps and advises when- ever I needed. They supported by reminding me of Dharma- the tool to cure my mind. I always remember their kindness and friendship. My stay in Cleveland will be memorable forever. Last but not least, I am greatly indebted to my beloved parents and my brother for their unconditionally spiritual supports since I was born. My ways of living and thinking have been taught by my family, which is an essential part of my success. I believe this success is the one that my parents are waiting for and proud of. Now it is apparent that our dream comes true. Thank you for believing in me. Finally, after I stand every hardship to overcome the barrier of success, I have been essentially developed to be a potential human resource in order to contribute to my motherland.

xvii Mathematical model for hemodynamic and intracranial Windkessel mechanism

Abstract

THUNYASETH SETHAPUT

The understanding of intracranial system so that one can explain its related pathological condition such as hydrocephalus and traumatic brain injury (TBI) is still sub- tle. Especially, the cause of hydrocephalus which is known as the common birth defect is not well defined. Traditionally, hydrocephalus was described as imbalance between production and absorption process of cerebrospinal fluid (CSF). However, many recent observations show that the bulk flow theory can no longer explain the cause of hydrocephalus. Hence, the new concept of hydrocephalus has been deviated from the bulk flow theory and comes to focus on the pulsatile dynamic of intracranial system and abnormalities of intracranial Windkessel mechanism. Windkessel mechanism is normally observed in major arterial system as well as intracranial space which is the absorbing function of artery provided by its elastic properties and peripheral resistance. The effectiveness of Windkessel mechanism can convert the pulsatile nature of blood flow generated by cardiac cycle into nearly pulseless outflow to capillary bed. Thus, the simulation via mathematical model based on Windkessel mechanism, which is one of the most useful tool to clarify the pulsatile dynamic within intracranial cavity is proposed. The mathematical model is constructed based on the mechanical and fluid mechanics principles to predict the hemodynamics throughout major arterial system and intracranial space. For intracranial system, the dynamical interaction

xviii among major intracranial contents and intracranial pressure (ICP) is simulated. Also, the constraints of Monro-Kellie doctrine is also another requirement to include in this model. To verify the model, the predicted results is compared to clinical data such as MRI data which have a good agreement. Typically, the intracranial disorders are associated with elevated intracranial pressure (ICP) and decreased cerebral blood flow. As the central nervous system (CNS) and brain require the sufficient cerebral blood supply to function normally, a marked reduction of cerebral blood flow known as stroke can result in the brain ischemia and further lead to a failure of brain’s neurological functions. For the patient with traumatic brain injury (TBI), an appearance of unilateral mass lesion such as hematoma is commonly observed. This mass effect can occupy the finite volume of intracranial space which reduces its volume compensatory capacity and brings about interhemispheric asymmetry of ICP and cerebral blood flow. The effect of an appearance of unilateral mass lesion on interhemisperic asymmetry of ICP and cerebral blood flow is also investigated. The significant difference of waveform and timing between two hemispheres is observed. This observation can be used as the indicator to predict and classify the patients with normal or abnormal intracranial Windkessel mechanism which is the useful information for real-time patient monitoring. As mentioned, the reduction of cerebral blood flow is typically observed in the patients with neurosurgical disorders, the medical balloon insertion is introduced as the alternative treatment. To recover the cerebral blood flow, the cadence balloon with inversion cycle provides the most significant improvement in the simulation results which support the possibility of using cadence medical balloon as the treatment options for the patient with decreased cerebral blood flow. According to the simulation results, the failure of intracranial Windkessel mechanism might be the key factor which provide the appropriate explanation to define the cause of hydrocephalus especially communicating hydrocephalus. The developmental cycle of hydrocephalus is also hypothesized. This hypothesis might explore the understanding and direct the effective treatment procedure for the patient who suffers

xix from disorder related to intracranial system.

xx Chapter 1

Introduction

1.1 Motivation and Literature Survey

Each year, a significant number of patients who suffer from the disorders associated with intracranial system was reported. In the United States, traumatic brain injury (TBI) is a contributing factor to one thirds (30.5%) of all injury-related deaths [50]. The Centers for Disease Control and Prevention has estimated that an approximately 1.7 million Americans sustain a TBI-related emergency department visits (about 1.365 million), hospitalizations (about 275,000 cases), and deaths (about 52,000 cases) annually [50]. Another well known neurosurgical disorders which label as one of the most common birth defects is hydrocephalus. According to the World Health Organization (WHO) hydrocephalus statistics show that one birth in every 2,000 are affected by hydrocephalus. However, hydrocephalus can occur at any age, but is most commonly occur in infants or the elderly. In the United States, approximately 69,000 hospital discharges with the diagnosis of hydrocephalus have been reported annually [136]. In 2003, there were 38,200 to 39,900 admissions for pediatric hydrocephalus which ac- counted for 0.6% of all pediatric hospital admissions in the United States [155]. The American Hydrocephalus Association has estimated that an approximately 375,000 older Americans suffer from normal pressure hydrocephalus (NPH). In addition, the

1 pediatric center for Intermountain Healthcare, a health care system in the Intermoun- tain West (Utah, Montana,Idaho, Wyoming, and Nevada), estimated that the number of American people living in the United States and were treated for hydrocephalus ranged between 120,000 and 150,000 each year while one sixth of this group of patients were young adults between 18 and 35 years of age [154]. Hence, the number of young adults who have hydrocephalus, aged 18 to 35 needed treatment in the United States was predicted to exceed 40,000 annually within the next two decades [154] as shown in Figure 1.1. Nowadays, the causes of hydrocephalus are still not clearly understood. Hence, the lack of appropriate diagnosis and treatment often undergo.

Figure 1.1: Current and projected numbers of patients with hydrocephalus, aged 18 to 35, treated in the United States. Dark bars indicate projections of numbers of patients based on the actual numbers treated at Intermountain Healthcare; lighter bars indicate future projections for young adults with hydrocephalus. Data source from Intermountain Healthcare [154].

Hydrocephalus were clinically studied for almost a century but the cause and understanding of this disorder were still hassle. Conventionally, hydrocephalus was originally explained as the cerebrospinal fluid (CSF) bulk flow theory based on the animal experimentation by Dandy in 1914 [40]. The bulk flow theory considers the cause of hydrocephalus as an imbalance between CSF formation by choroid plexus

2 and absorption process at arachnoid granulation [66]. The definition of hydrocephalus as disorder of CSF circulation is able to provide the good explanation of obstructive hydrocephalus which is caused by an intraventicular obstruction of CSF. However, the modern clinical observation of CSF absorption accepts that the majority of CSF absorbs at the capillaries of the central nervous system and not at arachnoid granulation [61, 66]. Thus, communicating hydrocephalus cannot be simply explained by the CSF bulk flow theory alone. According to clinical MRI data and experiments, new attention of hydrocephalus was focused on the pulsation of intracranial dynamics to explain the phenomena. Gre- itz et al. [61, 63, 65, 66] explained that communicating hydrocephalus was caused by abnormality of intracranial pulsations which was associated with intracranial Wind- kessel mechanism. Windkessel mechanism was the pulsation absorbing function of elastic arterial wall that could be observed in aorta and large arteries on entire body as well as intracranial cavity. The effective Windkessel mechanism was able to convert the pulsatile nature of arterial inflow into a continuous and almost pulseless outflow to capillary. Most important parameters describing intracranial Windkessel mechanism was its elasticity of intracranial contents referred to intracranial compliance. Decreased intracranial compliance leds to the breakdown of the intracranial Wind- kessel mechanism which caused dramatic changes in intracranial system including properties and pulsatile dynamics of flow and pressure. This might be one of the key concepts to explain the causes of communicating hydrocephalus. The major function of cerebral blood flow is to supply oxygen and other nutrients to the central nervous system (CNS) and remove carbon dioxide and other metabolic end products from the CNS which required a steady blood supply to maintain well neurological function of CNS. However, the malfunction and destruction of any contents within closed cranium commonly observed in the patients with neurosurgical disorders leads to the reduction of cerebral blood flow. Decreased cerebral blood flow normally known as cerebrovascular accident or “stroke” may result in secondary cerebral ischemia and then a failure of brains neurological function due to insufficient

3 oxygen supply. In the patients with TBI, an appearance of mass lesion due to the abnormal collection of internal bleeding blood (hemorrhage) brings about the compression of cerebrovascular bed and variation of intracranial dynamics. Moreover, the marked enlargement of cerebral ventricles with an excess accumulation of CSF observed in hydrocephalic patients might compress cerebral blood vessel between the rigid cranium and the ventricular dilation. Hence, a space-occupying effect produced by mass lesion or enlarged ventricles will exert the force on the surrounding brain parenchyma, resulting in collapsing of cerebrovascular system. In order to respond to the intracranial space occupation, reduced cerebral blood flow, elevated intracranial pressure (ICP) and brain herniation may occur after injury. Generally, cranium is considered as a single rigid compartment with uniform distribution of intracranial pressure (ICP) over entire intracranial space [39]. However, significant differences in ICP between left and right hemispheres (interhemispheric ICP gradients) were reported in many animal experimentations and clinical observations. In head-injured patients, a formation of hematoma from bleeding blood in the injured hemisphere (unilateral mass lesion) exerted an irregular force to occupy the space within a finite volume of the cranium which distorted the intracranial dynamics. Typically, a large expansion of unilateral mass lesion also brought about an appearance of midline shift over its center line on CT scan image. Furthermore, the reduction of global cerebral blood flow was typically found in clinical case reports of the patients with TBI and hydrocephalus. In the studies of regional cerebral blood flow, the interhemispheric asymmetry of cerebral blood flow was also observed in the patients who suffered from unilateral mass effect. However, the understanding of the interhemispheric asymmetry of ICP and cerebral blood flow which depended on various physiological factors and a wide variation of anatomical lesions were still unclear. For the patients with TBI or hydrocephalus secondary to tumor or mass effect, the practical treatment is to remove the cause of intracranial space occupation. Also, the treatment focuses on handling elevated ICP and maintaining adequate cerebral blood

4 flow to normal level to prevent the secondary injury and repair the damaged neurons. Shunting is commonly used to relieve the patients who suffer from hydrocephalus with high success rate when the cause of hydrocephalus is revealed. Removal of excess intracranial CSF and transport it into the bloodstream or other body cavities that compress intracranial vessel by shunt placement can recover intracranial compliance and consequently restore normal cerebral blood flow and hemodynamics conditions [62, 64, 68]. However, there are many complications associated with shunting procedures including shunt dependency, infection, over-drainage of CSF and development of the slit ventricle syndrome (SVS) [180]. Moreover, no significant improvement of CBF after shunting was observed in many case reports [72, 88, 109, 116, 127]. Since the cause of communicating hydrocephalus is inexplicit, shunting is only a symp- tomatic treatment of hydrocephalus [66]. For more effective diagnosis and treatment of communicating hydrocephalus, the complex dynamical system related to intracranial Windkessel mechanism should be reconsidered. A very useful tool to understand the intracranial system and its Windkessel mechanism is mathematical model. Early mathematical models for intracranial system focused on the bulk flow theory and multi-compartmental lumped model. However, as mentioned above, the new concept to define the cause of hydrocephalus focused on the pulsatile nature of intracranial contents. Hence, the pulsatility model of intracranial system should be introduced to facilitate the understanding of the interaction between intracranial contents during cardiac cycle. Based on the equivalent electrical circuit, Egnor et al. [46, 47] recently proposed the model of intracranial pulsation as a simple spring mass system. They also concluded that communicating hydrocephalus was resulted from the abnormalities of intracranial Windkessel mechanism. However, the effect of compliance and blood volume alterations on intracranial dynamics was not included which was the limitation of this electrical circuit model. To understand intracranial dynamics based on Windkessel mechanism, the variation of arterial and intracranial compliance and cerebral blood volume might be the significant factor. Thus, mechanical model based on fluid dynamics principles which

5 describes the eﬀect of vascular expansion and compression on intracranial pulsation should be constructed. Also, the dynamical interaction to compensate the volumetric change of intracranial contents within a rigid container of cranium according to Monro-Kellie doctrine is another important constraint to be satisﬁed. The purposes of this dissertation are as follows:

• to elaborate hemodynamics through human major arterial system and intracranial space based on Windkessel mechanism using mathematical model

• to investigate the interaction among intracranial pressure (ICP) and main intracranial contents based on Monro-Kellie doctrine

• to compare intracranial dynamics response for diﬀerent intracranial conditions

• to identify the interhemispheric asymmetry of ICP and cerebral blood ﬂow due to an appearance of unilateral mass lesion

• to assess the possibility of medical balloon insertion with cadence action in intracranial cavity on cerebral blood ﬂow improvement

• to provide the hypothesis of the cause of hydrocephalus related to intracranial Windkessel mechanism

1.2 Contributions

The major contributions of this dissertation can be summarized as follows:

• Based on Windkessel mechanism, hemodynamics through major arterial system and intracranial cavity is scrutinized by using mathematical model. It shows that the development of mathematical model governing by fluid mechanics and mechanical principles is the effective tool to study the behavior of blood flow through arterial and intracranial system.

6 • Intracranial dynamic response of intracranial pressure (ICP) and major intracranial contents in waveform and timing aspect are proposed. As well as, in term of timing and waveform, the relationship of ICP signal and blood ﬂow at femoral artery is compared in normal condition. The interactional relationship within intracranial space provides the dynamical understanding of intracranial system in healthy patients which the fundamental information for further studies related to pathological condition.

• The effect of unilateral mass lesion on intracranial dynamic especially interhemispheric asymmetry of ICP and cerebral blood flow is observed. In addition, the relationship between the size of mass lesion and interhemispheric asymmetry of ICP and cerebral blood flow is investigated. This observation can assist the health care providers to predict the patient outcome and directly focus on the proper target for treatment.

• The abnormalities of intracranial Windkessel mechanism due to space occupying mass lesion is analyzed. Many simulation results can be used as the indicators to predict the failure of intracranial Windkessel mechanism which is valuable information for real-time patient monitoring.

• To improve cerebral blood ﬂow, the alternative treatment using a medical balloon insertion with cadence action is applied which enhances the possibility to use the balloon in the patient with decreased cerebral blood ﬂow.

• The cause of hydrocephalus especially communicating hydrocephalus is hypothesized. The breakdown of intracranial Windkessel mechanism might be the factor associated with the causation of hydrocephalus. Also, this hypothesis might provide the eﬀective direction for the treatment of hydrocephalic patients.

7 1.3 Outline of the Dissertation

This dissertation is organized as follows:

• Chapter 1: Introduction In this chapter, the motivation of this dissertation is presented which includes the disorder related to intracranial system and its understanding. The concept of mathematical model to understand the intracranial system dynamically is also introduced. Furthermore, the major purposes and contributions are summarized.

• Chapter 2: Review of Physiology An overview of the physiological background associated with hemodynamics and intracranial system is introduced which consists of major contents of cardiovascular system and intracranial space. This information provides the physiological parameters used as reference for constructing mathematical model. Common pathological conditions related to intracranial system and treatment procedure are also brieﬂy reviewed.

• Chapter 3: Associated Intracranial System In order to describe the hemodynamics of major arteries and intracranial space, a concept of Windkessel mechanism is introduced. Moreover, main principles and constraints involved in the dynamic of intracranial system are presented. In clinical and experimental observation, the change in intracranial dynamics and Windkessel mechanism with common techniques for assessment its abnormality are reviewed. This chapter also includes the eﬀects of pathological conditions on interhemispheric asymmetry of intracranial pressure (ICP) and cerebral blood ﬂow. This behavior of hemodynamics and intracranial system with its abnormality is essential for modeling the dynamics simulation.

• Chapter 4: Review of Windkessel Model and the Model of Intracra- nial System

8 In this chapter, some early mathematical models related to intracranial system are reviewed which are divided into two sections. First, Windkessel model is the mathematical model to describe the hemodynamics through arterial system represented by the electrical element in the simple RLC circuit. Second, the model of intracranial system is reviewed which is categorized into two major types of modeling to describe the behavior of intracranial system: (1) complex compartmental model and (2) pulsatility model.

• Chapter 5: Mathematical Model Based on Windkessel mechanism, the mathematical model of hemodynamics through major arterial system and intracranial space is developed. The principles of mechanical and fluid mechanics is applied in this pulsatility model to explain the hemodynamics and the interaction among intracranial contents and intracranial pressure. In this chapter, the effects of intracranial space occupation on interhemispheric asymmetry of intracranial pressure and cerebral blood flow and the improvement of cerebral blood flow by using medical balloon are also investigated.

• Chapter 6: Simulation Results The simulation mainly focuses on three cases including (1) normal condition, (2) neurosurgical condition, and (3) treatment by using a medical balloon. For normal condition, the hemodynamics downward through major arterial system to femoral artery and upward to intracranial space are presented. For neurosurgical condition, the simulation results show the effects of an appearance of unilateral mass lesion on intracranial dynamics, as well as the interhemispheric asymmetry of intracranial pressure and cerebral blood flow. Also, the effects of mass lesion size on the dynamics of intracranial system are demonstrated. In case of treatment, the results show that an insertion of medical balloon with intermittent action is related to the improvement of cerebral blood flow. Addi- tionally, the results predicted by mathematical model are compared to clinical

9 and experimental observations which are in good agreement. According to simulation results, the unknown cause of hydrocephalus especially communicating hydrocephalus is hypothesized which related to the failure of intracranial Wind- kessel mechanism. This hypothesis might be essential for future prevention and treatment of patient with hydrocephalus.

• Chapter 7: Summary and Conclusions The results of this dissertation are summarized, and further research direction are suggested.

• Appendix: Parameters for the Model of Hemodynamics and Intracra- nial System Table of the parameters which used for constructing the mathematical model is presented.

10 Chapter 2

Review of Physiology

In order to understand and see a clear picture of the intracranial system and its relevant, a brief background of human physiology is necessary. This section provides a basic knowledge of cardiovascular system and intracranial space including brain and intracranial ﬂuid. Moreover, the pathological conditions associated with intracranial system and their practical treatment methods are reviewed

2.1 The Cardiovascular System

In human cardiovascular system, heart and an extensive network of blood vessels are the main components to circulate blood throughout the body for distribution of oxygen via respiration system and nutrient transportation via digestive system which regulates body temperature, and distributes hormones and other agents that regulate cell function [10]. The closed loop of circulatory system is divided into the pulmonary circulation and the systematic circulation. The role of pulmonary circulation is to carry the de-oxygenated blood from the heart, to the lungs where gas exchange can occur, and return the oxygenated blood to the heart. The function of systematic circulation, which contain about 84 percent of the entire blood volume of the body [69], is to supply blood to all the peripheral organs and tissues of the body. The heart and circulation are controlled, to provide the necessary cardiac output and arterial

11 pressure [69], by multiple regulatory systems that function in general to maintain adequate capillary blood ﬂow when possible in all organs, but particularly in the heart and brain [10].

2.1.1 Heart

The heart, consists primarily of a special type of muscle called cardiac muscle, is the major source of squeezing power to provide blood ﬂow through the entire bodys circulatory system. The pumping action of the heart is pulsatile rather than continuous [78]. The heart intermittently pumps the volume of oxygenated blood throughout the body in the time interval of a minute called “cardiac output” (Figure 2.1). The cardiac output of a healthy adult, at rest, is approximately 5 liters (L) of blood per minute [148]. The cardiac cycle, the cardiac events that occur from the beginning of one heartbeat to beginning of the next [69], consists of a period of ventricular relaxation during the heart chambers reﬁll with blood called “diastole” followed by contraction of the heart ventricles called “systole” which pumps blood into circulatory system. The frequency or discharge rate of the recurring cardiac cycle is described by the heart rate, the number of beats the heart contracts per minute. Heart rate in normal adults is about 72 beats/min, each cardiac cycle lasts approximately 0.8 s, with 0.3 s in systole and 0.5 s in diastole [193]. The stroke volume is the volume of blood ejected from each heart’s ventricle per stroke during systole which can be calculated by substracting end-diastolic volume by end-systolic volume. The stroke volume in a healthy man at rest is approximately 70 ml, end-diastole volume is 135 ml, and end-systolic volume is 65 ml [193]. Thus, the cardiac output (L/min) can be calculated by multiplying the heart rate (beats/min) and the stroke volume (L/beat).

2.1.2 Vascular System

Blood vessels are a tubular closed-loop network that carry blood from the heart to the tissue and back to the heart. Blood leaving the heart passes through vessels

12 Figure 2.1: Pulsatile blood flow in the root of the aorta recorded using an electro- magnetic flowmeter [69]. of progressively smaller diameters, referred to as arteries, arterioles, and capillaries. Then, blood returning to the heart from the capillaries pass through vessels of progressively larger diameters, called venules and veins. The structural characteristics of the blood vessels change with successive branching [193] which reflect their function. The characteristics of various types of blood vessels are listed in Table 2.1. Because of the different total cross-sectional area of blood vessels, the blood flow velocity is very high in aorta and progressively slow in arteries. Then, flow velocity is markedly slow while passing through capillaries due to their larger total diameter, and become higher again when flow through veins. The force that blood applies to the wall of a blood vessel in known as blood pressure. Blood pressure varies throughout the cardiovascular system, being the highest in the aorta and large arteries (120 to 80 mmHg), lower in the capillaries (35 mmHg near the arteriolar ends to as low as 10 mmHg near the venous ends [69]), and the lowest in vein as shown in Figure 2.2. Since the pumping action of heart is pulsatile, the peak arterial pressure level reached during ventricular contraction to eject blood from the heart refers to systolic pressure. The minimum arterial pressure level, occurs during ventricular diastole before next ventricular ejection begins, refers to diastolic pressure. In a young adult human, the systolic arterial pressure in the aorta and in the large arteries is about 120 mmHg and diastolic pressure is about

13 Table 2.1: Characteristics of various types of blood vessels in humans [10].

80 mmHg [78]. The arterial pressure conventionally written as systolic pressure over diastolic pressure [10], for example, 120/80 mmHg. The diﬀerence between systolic pressure and diastolic pressure is called the pulse pressure [193], about 120 - 80 = 40 mmHg.

Figure 2.2: Blood pressure in diﬀerent segments of the vascular system [78].

14 Arteries

The major function of the systemetic and pulmonary arterial systems is to transport blood to various capillary beds. Under high blood pressure condition, the thick mus- cular walls of the aorta and other large arteries, contain a relatively large amount of elastic tissue; however,the walls of the arterioles,the last small branches of the arterial system, contain less elastic tissue but much more smooth muscle [10]. Due to elastic properties of arterial wall of the aorta and the other large diameter arteries, they act as pressure reservoir for maintaining blood flow through the tissues during diastole [193] because the volume of blood pumped into can be stored in them with each cardiac cycle. Also, they act as a hydraulic filter because they converts pulsatile flow generated by heart to the continuous steady state flow through capillaries. The contraction of ventricles ejected blood into arteries and then arterial walls are stretched to accommodate the extra blood volume, and arterial blood pressure rises during systole. When the ventricular contraction ends, the stretched arterial walls recoil passively and blood continues to be driven into the arteries and flow out to capillaries during diastole as shown in Figure 2.3. As blood leaves the arteries, the arterial volume and pressure slowly fall, but the next ventricular contraction occurs while there is still adequate blood on the arteries [193]. The term used to describe the distensibility of artery or how easily an artery can be stretched is compliance. An artery with high compliance can be stretched very easily. Compliance (Compliance =∆V olume/∆Pressure) can be defined as the total quantity of blood that can be stored in a given portion of the circulation for each unit of pressure rise [69]. Hence, arterial blood volume and arterial compliance are two main physical factors that determine arterial pressure. Stroke volume, speed of ejection of the stroke volume during systole, and arterial compliance are the most important physiological factors that affect the magnitude of arterial pulse pressure [193]. In hemodynamics studies, the transmission of pulse pressure while traveling from heart to aorta through the progressively smaller blood vessel can be expressed in term

15 Figure 2.3: Movement of blood into and out of the arteries during the cardiac cycle. The lengths of the arrows denote relative quantities flowing into and out of the arteries and remaining in the arteries [193]. of blood inertia that prevents sudden blood movement all the way to the periphery [69] as shown in Figure 2.4. Thus, the transmission of pulse pressure is slow in the large blood vessel with high compliance; however, the transmission become faster in the smaller blood vessel with lower compliance. Also, the progressively less pulsatility of prssure pulse, described in term of damping of the pressure pulse, when blood flow toward the smaller vessels almost directly depend on their resistance and compliance [69]. Greater resistance or compliance result in greater degree of damping of the pressure pulse. Because an immediate change in arterial blood pressure causes drastic change in blood flow; however, most blood vessels have an intrinsic capacity to compensate for change of arterial pressure to regulate blood flow to normal level by changing in vascular resistance through its radius. This intrinsic regulatory mechanisms that maintain blood flow and circulation against changes in systemic arterial pressure called “au-

16 Figure 2.4: Changes in the pulse pressure contour as the pulse wave travels toward the smaller vessels [69]. toregulation”. The autoregulation reacts to a variation of systemic arterial pressure by automatically expansion of arteries when blood pressure fall and contraction when pressure rise.

Capillaries

Thin-walled vessels of capillaries form branching networks, known as capillary beds, among the cell of body tissues. Approximately 5 percent of the total circulating blood is ﬂowing through the capillaries [193]. The extensive porous walls branching of capillaries provide very small diﬀusion distances to body cells which allow nutrients and metabolic end product (waste product), such as carbon dioxide and urea, to exchange between cells of the body and blood. Low blood pressure in the capillaries

17 enhances the rate of exchange between blood and tissues. Also, the large total cross- sectional area of capillaries result in the slowest ﬂow velocity while passing through capillaries to provide the time availability for substances to exchange between the blood and interstitial ﬂuid [193]. In the lungs and in highly metabolic tissues, such as the liver, kidneys, skeletal muscle, and cardiac muscle, capillaries form more numerous and more extensive networks than in other tissue types [148].

Viens

The veins are the last set of vessels through which blood flows on its way back to the heart. A major function of the veins is to act as low-resistance conduits for blood flow from tissue to the heart [193]. The wall of veins are thinner and much more compliant than arteries, therefore maintaining peripheral venous pressure and facilitating venous return to the heart are the additional functions of veins. Veins also serve as blood reservoir for the circulatory system [69] because they can accommodate large volume of blood (approximately two-thirds of the total blood volume [78]) with relative small increase in internal pressure. The contraction of the veins, called venous pump [69], decrease the diameter and compliance of the vessels and raise the venous pressure to propel more blood out of the vein into the right heart. Not only pressure difference between the peripheral veins and the heart, and the mechanism of venous contraction assist the veins in returning blood to the heart, but one-way valves inside the veins also prevents backflow and allows blood to flow in one direction only toward the heart [78]. In nearly rigid intracranial space, venous blood is able to compensate for the arterial pulsations because intracranial pulsation from nearby artery may compress veins.

18 Major Arteries of the Systemic Circulation

In systemic circulation (Figure 2.5), the blood flow from the heart through the first set of systemic blood vessel called aorta which usually considered in three parts: the ascending aorta, the aortic arch and the descending aorta [148]. Blood, after passing through the ascending aorta and then the aortic arch, flow to two major parts of the body which are the head and upper limbs, and the abdomen and lower limbs by following pathways:

Arteries of Head, Neck and Upper Limbs

The brachiocephalic artery is the ﬁrst short artery branch of the aortic arch. The brachiocephalic artery divides into the right common carotid artery, which transports blood to the right side of head and neck, and right subclavian artery, which transports blood to the right upper limb [148]. However, to supply blood to the left side of head, neck, and the upper limb, the left common carotid and subclavian artery branch directly oﬀ the aortic arch with no brachiocephalic artery. In each side of neck, the common carotid arteries branch into several branches of external carotid arteries which supply blood to the structure of the neck, face, nose, and mouth [148], and internal carotid arteries which is the major arteries that supply to the brain via the carotid canals. Blood supply to each side of the upper limb through the subclavian artery, followed by axillary artery, brachial artery, ulnar artery and radial artery which supply blood to the forearm and hand.

Arteries of Abdomen and Lower Limbs

The ﬁrst artery from the aortic arch that transport blood through the chest and abdomen to lower limbs called descending aorta. The descending aorta, the longest part of the aorta [148], is divided into two portions: a thoracic aorta which located between thorax and thoracic diaphragm, and an abdominal aorta which located in the abdominal cavity. The abdominal aorta, then, branched into two common iliac

19 Figure 2.5: The major arteries that carry blood from the left ventricle of the heart to the tissues of the body [148].

20 arteries. Also, each common iliac artery (left and right) divides into an internal iliac artery to supply blood for pelvic area, external iliac artery to supply blood for the lower limb. The external iliac artery further connect to the femoral artery in th human thigh, and the extension of femoral artery called popliteal artery. The popliteal artery bifurcates into anterior and posterior tibial artery for transporting blood to the feet.

2.2 Intracranial Space

The intracranial space or cranial cavity is the space formed inside the skull. The volume of intracranial space is approximately 1,600-1,700 ml [69] in average adults. The normal contents of the intracranial space are brain, spinal cord, cerebrospinal ﬂuid (CSF) and cerebral blood.

2.2.1 Brain

The brain is part of the central nervous system (CNS) which receives sensory information in the form of action potentials from various nerves and the spinal cord, integrates it, and generates the appropriate response, so that it is well protected against physical injury and disease [78]. The brain, weighs about 1400 g [10], is housed by the skull, a rigid bony closure that protects it from injury. As shown in Figure 2.6(a), the brain can be subdivided into four major subdivisions: cerebrum, diencephalon, brainstem, and cerebellum [193]. The composition of cerebrum and diencephalon called the forebrain. The brainstem can be divided into three regions: the midbrain, rostral to the pons and continuous with the diencephalon; the pons, rostral to the medulla oblongata; and the medulla oblongata, rostral to and continuous with the spinal cord [152]. The brainstem connects the spinal cord to the remainder of the brain and contains several nuclei involved in vital body functions such as the control of heart rate and breathing [148]. The additional protection of brain and spinal cord is provided by a watery liquid called cerebrospinal ﬂuid (CSF) and membranous covering called meninges. As pre-

21 (a) (b)

Figure 2.6: (a) The surface of the cerebral cortex and the divisions of the brain shown in sagittal section [193], (b) Investing membranes of the brain, showing their relation to the skull and to brain tissue [10]. sented in Figure 2.6(b), Meninges consists of three layers of connective tissue: dura mater, arachnoid mater, and pia mater next to the nervous tissue. The dura mater, the most superficial and thickest of the meninges, around the brain is tightly attached to the periosteum of the skull [148]. The space between the arachnoid and the pia mater, known as subarachnoid space (SAS), is filled with CSF and contains cerebral blood vessels. The brain is supported within the arachnoid by the cerebral blood vessels and nerve roots and the multiple fine fiberous arachnoid trabeculae [10]. These trabeculae arise from the arachnoid, span the subarachnoid space,and then connect with the pia, help to keep the brain suspended within the meninges [152]. The brain also contains four interconnected CSF-filled cavities called the cerebral ventricles which are the main components in CSF circulating process. The cerebral ventricles consist of two large lateral ventricles located in each cerebral hemisphere, the third ventricle which is a smaller midline cavity located within the center of the diencephalon between the two halves of the thalamus, and the fourth ventricle located at the base of the cerebellum [148].

22 2.2.2 CSF and Ventricular System

Cerebrospinal fluid (CSF) is clear and colorless fluid. However, it may be colored in pathological conditions; for example, several hours after subarachnoid hemorrhage results in the yellow color of CSF [152]. The CSF is similar to the interstitial fluid that bathes all cells, but it does not exchange substances as freely with blood [78]. In normal adults, the volume of CSF is about 90-140 ml which contains within the cerebral ventricles about 23 ml and and the remaining is in the subarachnoid space of brain and spinal cord [152]. Because of the specific gravity of the brain and the CSF are approximately equal (only about 4 percent different), the brain simply floats in the CSF [69]. Due to the buoyancy or floating of the brain in the CSF, the brain has a net weight of only 50 g compared to 1400 g of the weight of brain in air [10]. Also, this buoyant effect of the CSF can reduce the traction exerted on the nerves and blood vessels connected with the CNS [152]. The major function of the CSF is to protect brain from physical traumas of ev- eryday living by cushioning the brain within rigid skull. Without this protection of CSF and meninges, the brain can be easily damaged even by minor head injury [10]. In the normal healthy person, the normal pressure in the cerebrospinal fluid system, may refer to intracranial pressure (ICP), is about 10 mmHg [69]. An enlargement of size or volume of any intracranial contents can cause an increase in ICP [152]. High ICP result from many pathological conditions of the brain such as brain tumor, hemorrhage inside the cranium, and also hydrocephalus which sometimes elevates the ICP about four times over its normal pressure [69]. Because of the cranium is the rigid chamber which does not allow any physical swelling toward outside, so the elevated ICP is the unique problem compared with similar situations elsewhere in the body [193]. The increased ICP exerts a collapsing force on intracranial vasculature. The smaller radius of blood vessel greatly increases the resistance of blood flow to the brain, and also reduce the cerebral blood flow below the level needed to satisfy metabolic requirements [193]. An increased ICP may cause the following symptoms:

23 headache, nausea, vomiting, loss of consciousness, and an increase in systemic blood pressure [152]. In practice, the only way to restore brain blood ﬂow at a normal mean arterial pressure is to remove the tumor or accumulated ﬂuid [193].

Formation, Flow, and Absorption of Cerebrospinal Fluid

The rate of CSF production, relatively constant regardless of systemic blood pressure or intraventricular pressure [28], is approximately 500 ml/day for normal adults which is three to four times as much as the total volume of fluid in the entire cerebrospinal fluid system [69]. Thus the CSF turns over about 3.7 times a day [10]. In experiments on animals, approximately 50-70% of CSF is produced and secreted by the epithelial in the wall of the four ventricles called “choroid plexus” and the remainder of CSF is formed around blood vessels and along ventricular walls [10]. Choroid plexus produces the bulk flow of CSF and the pulsatile flow of CSF is provided by active secretion from cardiac pulsation. During systole, the expansion of choroid plexus with arterial blood generate a pressure pulse to the CSF. Hence, the choroid plexus play a role as a pump to stimulate the CSF circulation in ventricular system.

(a) (b)

Figure 2.7: (a) The pathway CSF ﬂow from the choroid plexus in the lateral ventricles to arachnoid villi penetrating into sagittal sinus [69]. (b) Ventricular system of the brain [173]

As illustrated in Figure 2.7, the normal circulation of CSF ﬂows from the two lateral ventricles (left and right) to the third ventricle through the two cavities of

24 foramen of Monro where it mixes with more CSF [152]. Then, CSF flows from the third ventricle into the fourth ventricle via cerebral aqueduct or aqueduct of Silvius which is the narrowest CSF pathway in the ventricle system. The flow of CSF from the fourth ventricle is transmitted to the subarachnoid space (SAS) that surround the brain and the spinal cord by using the pathway of foramina of Magendie and lateral foramina of Luschka. Some CSF flow around the tentorium upwards for absorption process at the superior sagittal sinus. Some CSF flow downward into the basal cisterns and spinal subarachnoid space. For downward flow, the pressure- volume compensatory mechanism may take place to compensate the expansion of lumber space by elasticity of spinal theca which act to dampen the cerebral arterial pulse [38, 66]. Thus, the elasticity of spinal theca is one of the most important element of the intracranial Windkessel mechanism which allow the pulsatile energy of CSF flow from the intracranial space to absorb in the spinal subarachnoid space. The conventional bulk flow theory of CSF believe that the major absorption into venous system of CSF penetrate the sagittal sinus’s wall via arachnoid granulation or arachnoid villi. This drainage, follows the hydrostatic pressure gradient principle between CSF and venous sinuses pressure, transport when subarachnoid ICP is higher than sigittal sinus pressure and stop otherwise. However, the modern concept of CSF absorption accept that the majority of CSF absorb at the capillaries of the central nervous system based on the Starling principle [61, 66].

2.2.3 Cerebral Blood Flow

The metabolic demands of the brain must be met with the blood supply to this organ with normal cerebral blood ﬂow is about 50 mL/100 g of brain tissue/min [152]. With average weight of brain about 1,400 - 1,500 g, the average cerebral blood ﬂow for the whole brain is about 700 to 750 ml/min [152] or about 15 percent of total cardiac output at rest [69]. Most of the blood supply to brain (about 350 ml/min [152]) via two internal carotid (left and right) arteries which branch from each side of common carotid arteries. Some of the blood to the brain is supplied by two vertebral

25 arteries which branch arising from each side of subclavian arteries [148]. Then, the two vertebral arteries combine at the caudal of the pons to form a single basilar artery [152]. The combination of two internal carotid arteries and vertebro-basilar system (two vertebral arteries and a basilar artery) form a circle of blood vessel to supply blood to the brain called the cerebral arterial circle [148] or the circle of Willis as shown in Figure 2.8.

Figure 2.8: The internal carotid artery and vertebro-basilar system. Note the cerebral arterial circle (circle of Willis; marked by a dashed black line) [152].

A unique characteristic of the cerebral circulation is that it all envelopes within a rigid cranium. According to Monro-Kellie doctrine, the volume of cerebral blood, CSF, and brain in the rigid cranium is relatively constant at any time; changes in either of these ﬂuid volumes must be coincident with a reciprocal change in the other. Hence, cerebral blood supply can be interrupted by many risk factors such as an excessive accumulation of CSF within the brain referred to hydrocephalus or

26 a bleeding of cerebral blood vessel resulting from head injury referred to intracranial hemorrhage. A brief cessation of cerebral blood flow to central nervous system as little as 10 minutes may cause loss of consciousness and serious neurological disorders. A blood supply to the brain below the level of 25 ml/100 g of brain tissue/min can lead to ischemic penumbra [152], a condition of inadequate blood to meet brain’s metabolic demand, and further result in the irreversible brain tissue damage and loss brain function due to insufficient oxygen supply. Also, a blood flow to brain below 8 ml/100 g of brain tissue/min leads to an almost complete loss of functional neurons [152].

2.3 Pathological Conditions

As mentioned, the major function of cerebral blood ﬂow is to supply oxygen and other nutrients to the central nervous system (CNS) and remove carbon dioxide and other metabolic end products from the CNS which required a steady blood supply (about 15% of the cardiac output at rest) to function normally. The malfunction and destruction of any contents within closed cranium aﬀect their dynamics and lead to cerebral blood supply decrease which is normally known as cerebrovascular accident or “stroke”.

2.3.1 Stroke

Due to reduced cerebral blood flow, the delivery of oxygen and other nutrients to the brain is reduced and the carry of carbon dioxide and other waste products away become slower which greatly increase in the local concentration of carbon dioxide [69]. The condition of insufficient oxygenated blood supply to the brain is called brain ischemia. In addition, prolonged brain ischemia can lead to a failure of brain’s neurological functions and localized neuronal tissue death called brain infarction or cerebral infarction [152]. Cerebral strokes can be classified into two major causes: 1) ischemic stroke, resulted from blockage of arteries supplying brain tissue, and 2)

27 hemorrhagic stroke, resulted from rupture of cerebral arteries that bleeding into the brain.

Ischemic Stroke

Ischemic stroke or occlusion stroke accounts for about 85% of all cases of stroke [58]. Ischemic strokes are generally caused by an obstruction of blood flow within the artery that supply blood to the brain resulting from the accumulation of fatty deposits such as cholesterol called atherosclerotic plaques. For example, the person who suffers from a blockage of the middle cerebral artery on the left hemisphere becomes almost totally demented because the lost of function in speech comprehension area and also unable to speak words because the loss of word formation function [69]. The blockage in ischemic stroke can result from two major subtypes of obstruction which are cerebral thrombosis and cerebral embolism. Cerebral thrombosis is a blood clot develops within a part of artery that supplies blood to the brain such as blockage of the carotid artery, called carotid atherosclerosis. About 23% of ischemic stroke originates from carotid atherosclerosis [58]. Cerebral embolism is a blood clot that forms or has detached from a larger clot elsewhere in the circulatory system (often a vein [78]) travels toward the brain until reach too narrow blood vessel to pass and finally lodge in and block the cerebral blood vessel [148]. Only small size of plaque can lead to dangerous clots, because the major arteries of the Circle of Willis have lumen diameters of <4 mm [58]. Risk factors for ischemic stroke include factor that raise degree of atherosclerosis such as high blood pressure (hypertension), diabetes, poor diet, physical inactivity, and obesity.

Hemorrhagic Stroke

Hemorrhagic stroke or bleeding stroke is caused by the bleeding of the blood within cranial space from the ruptured blood vessel. Hemorrhage can cause an intracranial mass lesion which is a mass eﬀect from the accumulation of bleeding blood. Most common type of intracranial mass lesion is hematoma. This abnormal collection of ex-

28 travascular blood (hematoma) inside the skull can compress the local brain tissue and increase intracranial pressure. Hemorrhagic stroke can be roughly categorized into two types which are intracerebral hemorrhage (ICH) and subarachnoid hemorrhage (SAH). Intracerebral hemorrhage (ICH) is the bleeding of blood within the brain tissue. ICH accounts for about 10-15% of all cases of stroke with approximately 77-78% of all ICH resulting from small intracranial blood vessel are ruptured by chronic hypertension (hypertensive hemorrhage) or cerebral amyloid angiopathy [153]. Up to 70% of patients with primary ICH is founded the expansion of hematoma over the initial few hours [43]. While, subarachnoid hemorrhage (SAH) is the bleeding of blood in the subarachnoid space which is CSF-ﬁlled space between the arachnoid and the pia. About 90% of SAH often occured in the Circle of Willis by a cerebral aneurysm (abnormal ballooning outward of the arterial wall) [129]. A formation of cerebral aneurysm results from a weakened portion of blood vessel which allow extravascular blood to ﬁll in and create a bulge of blood. Then, extravascular blood in aneurysm can leak into the surrounding subarachnoid space. Risk factors for ischemic stroke include the factors that raise degree of atherosclerosis such as high blood pressure (hypertension), diabetes, poor diet, physical inactivity, and obesity. Major risk factor for hemorrhagic stroke is also hypertension. However, two additional common causes of stroke ,especially hemorrhagic stroke, are traumatic brain injury (TBI) and hydrocephalus.

2.3.2 Traumatic Brain Injury

Traumatic brain injury (TBI) is a damaged injury to the brain resulting from external mechanical force. The major causes of TBI are: motor vehicle accidents, falls, violence, and sports injuries [110]. TBI can cause the internal bleeding (hemorrhage) from an injured blood vessel. The collection of bleeding blood brings about a formation of hematoma to occupy the space within the skull which has a ﬁnite volume. In order to response to the space-occupying intracranial lesion, elevated intracranial pressure (intracranial hypertension), brain herniation (displacement of brain), stroke, and

29 serious neurological deﬁcits may occur after injury. Not include subarachnoid hemorrhage, there are two dangerous forms of hematoma, located adjacent to the brain parenchyma, caused by TBI including epidural hematoma and subdural hematoma.

Epidural Hematoma

An epidural or extradural hematoma (Figure 2.9) is a collection of blood results from the loosening of the periosteal dura layer from the inner table of skull by the dissection of damaged artery [70]. The most common cause of an epidural hematoma is a skull fracture that results in bleeding of a major dural vessel, most notably the middle meningeal artery and about 15% of cases may result from a venous sinus bleeding [71]. These lesions tend to be smaller and more confined than subdural hematomas because the firm attachment of the dura layer to the inner table of the rigid skull is confined and may exert a closure effect to limit the size of the hematoma [129].

Figure 2.9: Axial noncontrast CT demonstrates an epidural hematoma [199].

30 Subdural Hematoma

A subdural hematoma is a collection of blood commonly caused by a rupture of the cortical bridging veins which flow within the subdural space through the subarachnoid space and drain toward superior sagittal sinus or other dural venous sinus [129]. Naturally, there is no occurring space between two layers of connective tissue of meninges which are dura mater and arachnoid mater [70]. However, this dura-arachniod space called subdural space will become a potential space and radi- ologically evident whereas there is fluid, hemorrhage or purulent material between the dura and arachnoid mater [129]. As shown in Figure 2.10, subdural hematoma appears long and thin compared to an epidural hematoma, along the entire surface of the brain [71]. Because of the relatively unconfined nature of the subdural space, subdural hematomas can be enlarged easily which brings about higher mortality rate compared to epidural hematomas [129]. Furthermore, a large expansion of these hematomas will exert mass effect on the surrounding brain parenchyma, resulting in compression of sulci and ventricle, or the presence of midline shift and herniation when severe [129]. As shown in Figure 2.10(b), an appearance of midline shift on CT scan occurs when an irregular force within the skull, resulting from the interruption of intracranial contents such as space-occupying lesion from brain tumor or hematoma, exert into brain to shift over its center line. The degree of midline shift depends on the size of mass lesion [3]. Because of essentially finite intracranial volume with 3 major intracranial contents (brain, CSF and blood) referred to Monro-Kellie doctrine, an expansion of any intracranial contents bring about compression of other contents. Moreover, volume compensatory capacity will be exhausted and result in elevated ICP. Large expansion of hematoma after brain injury may raise ICP over 30 mmHg which increase risk of transtentorial or brainstem herniation [192]. In patient with brain injury, reduced cerebral blood flow is commonly observed which may result in secondary cerebral ischemia. Thus, the treatment of TBI focus on handling elevated ICP and maintain-

31 (a) (b)

Figure 2.10: (a) Axial view of a subdural hematoma [110]. (b) Computed tomography indicated a large right-sided acute on chronic subdural hematoma (maximum depth, 1.9 cm) occupying the frontal, parietal and temporal convexities, and a possible small subarachnoid hemorrhage [196]. ing adequate cerebral blood ﬂow to normal level to prevent the secondary injury and repair the damaged neurons. To minimize this complication and increase chance of recovery, the prompt surgical treatment after a severe traumatic injury is required [192].

2.3.3 Hydrocephalus

Hydrocephalus is a clinical condition of the excessive accumulation of CSF within or around the brain. Currently, there is no obvious cause of hydrocephalus [142]. The traditional theory of hydrocephalus is generally understood as an imbalance between CSF formation and absorption and a disorder of CSF bulk flow circulation [66]. However, the new attention of hydrocephalus has focused on the pulsatile nature of the fluid flow and pressure within the intracranial cavity [46, 47, 66, 101, 106]. Due to blockage of CSF circulation with continuous production of CSF, hydrocephalus result in marked enlargement of cerebral ventricles (Figure 2.11) with an excess accumulation of CSF and then increase in ICP and CSF pulse pressure. Moreover, the

32 brain parenchyma and cerebral blood vessel might be compressed between the rigid cranium and the ventricular dilation lead to a progressive loss of brain neural function and reduction of cerebral blood flow. Hydrocephalus is common birth defects (one birth in every 2,000 results in hydrocephalus according to the World Health Organization studies) for unknown reasons [181] which may develop before birth or during the first few months [152]. In infant with stretchable skull bone, the cerebral ventricular dilation may lead to abnormal enlargement of head and damage the de- veloping brain. Traditionally, hydrocephalus can be classified as communicating and non-communicating based on its mechanism. Communicating hydrocephalus (non-obstructive) results from the accumulating in ventricles and cease of CSF-flow into the subarachniod space. Traditional theory believe that communicating hydrocephalus is caused by the functional impairment of arachnoid granulations or arachnoid villi where absorption of CSF into the venous sinuses occurs. However, new understanding of communicating hydrocephalus is caused by decreased intracranial compliance and restriction of arterial expansion as shown in Figure 2.12 [66]. Communicating hydrocephalus have a variety of causes such as tumors or infection involving in the CNS [70] which may cause adhesions to form in the subarachnoid space resulting in decreased intracranial compliance [66]. Also, communicating hydrocephalus can be caused by subarachnoid hemorrhage [129] which in 15-20 % of patients with SAH acutely develop communicating hydrocephalus [153]. One of the most common communicating hydrocephalus in the elderly is normal pressure hydrocephalus (NPH). NPH defined by gradual enlargement of the ventricles with excess CSF and slightly increase in ICP but still within the normal range. MRI data showed that patients with NPH have significantly lower vascular compliance than that of healthy individuals [11]. This reduction of vascular compliance decrease the amount of CSF flow downward to spinal cavity through the foramen magnum during systole [162]. NPH can be classified into two types: idiopathic and secondary. Idiopathic NPH (unknown cause of the disorder) is a condition of the elderly [134]. Secondary NPH is commonly caused by subarachnoid or intraventricular hemorrhage,

33 Figure 2.11: T1 weighted axial and sagittal magnetic resonance images of the brain in patients with ((b) and (d)) and without ((a) and (c)) hydrocephalus. The ventricles are markedly enlarged compared to normal. The cerebral aqueduct (arrow) is patent and there is no evidence of obstruction within the ventricular system. This is a case of communicating hydrocephalus [28].

34 Figure 2.12: Cerebral blood flow in (a) healthy individuals and in (b) communicating hydrocephalus. (a) The arterial windkessel mechanism, the wide intracranial vessels with small vascular resistance and the venous outflow resistance that keep the cerebral veins distended maintain the high normal blood flow. The venous outflow resistance is caused by a small positive intracranial pressure and is increased during systole. The venous outflow resistance is a mandatory prerequisite for the “waterfall phenomenon”, i.e. the pressure drop occurring from the cortical veins to the venous sinus. (b) In communicating hydrocephalus, the increased transmantle pulsatile stress (i.e. difference in pressure between ventricle and subarachnoid space) and the ventricular dilation compresses the cerebral veins and capillaries in their entire length. This significantly increases the vascular resistance and decreases the blood flow. The reduced venous outflow resistance facilitates collapse of the compressed capacitance vessels, which further decreases cerebral blood flow [66]. meningitis or head trauma [134]. Non-communicating hydrocephalus (obstructive), condition of the fluid accumulation within the ventricular system, result from the blockage of CSF-flow by obstruction of cerebral aqueduct or interventricular foramina (foramina of Luschka and Magendie) into subarachniod space either due to congenital malformations, external compression of CSF-flow pathways or intraventricular mass lesions (intraventricular hemorrhage) that disrupt the ventricular anatomy. Blockage of both interventricular foramina, for example by a congenital growth of colliod cyst (colloid tumor), will result in both lateral ventricle dilation [70]. However, unilateral obstruction of one interventricular foramina may results in enlargement of ipsilateral ventricle [70] called unilateral or monoventricular hydrocephalus as presented in Figure 2.13. For the acute phase of obstructive hydrocephalus, increased ICP are the most common clini-

35 Figure 2.13: (a) Preoperative MRI of a 7-year-old boy with monoventricular hydrocephalus due to shunt overdrainage: marked dilatation of the left lateral ventricle (b) MRI performed 10 days after the endoscopic fenestration of the septum pellucidum: marked decrease of size of the left lateral ventricle and reappearance of the subarachnoid spaces [55]. cal symptom [66]. For chronic obstructive hydrocephalus, the ventricular enlargement compress the brain parenchyma and cerebral veins which lead to decreased intracranial compliance and consequently a breakdown of intracranial Windkessel mechanism [66]. Thus, the hydrodynamics and clinical conditions of chronic obstructive hydrocephalus and communicating hydrocephalus are identical [66]. Hydrocephalus is commonly relieved by surgical interventions called shunt. Shunt is surgically implanted device used to bypass the obstruction and drain excess intracranial CSF and transport it into the bloodstream or other body cavities capable of absorbing the ﬂuid [28] such as the peritoneal cavity [38]. Removal of CSF that compress intracranial vessel by shunt placement can recover intracranial compliance and consequently normal cerebral blood ﬂow and hemodynamics conditions [62, 64, 68] by dilating cerebral veins or by reconnecting the free CSF communication between cranial subachnoid space and compliant spinal cavity [66]. This logical explanation support the view that communicating hydrocephalus is the disorder of intracranial pulsation [66]. Shunt also can be applied for other related diseases treat-

36 ment. However, there are many complications associated with shunting procedures including shunt dependency, infection, over-drainage of CSF and development of the slit ventricle syndrome (SVS) [180]. In addition, shunt placement in patients with subarachnoid hemorrhage from head injury can reduce CSF volume but increase the risk of brain herniation [192]. As commonly appearance of narrowed ventricles in patients with head injury, shunt become less eﬀective due to accessibility limitation [192]. There is no question that reliable shunt system can cure hydrocephalus problem especially obstructive hydrocephalus; however, shunt placement signiﬁcantly changes the pulsatility and dynamics of intracranial contents [180].

37 Chapter 3

Associated Intracranial System

Cardiac pumping action provides the pulsatile nature of arterial blood flow. However, capillary beds require continuous bulk flow for nutrient and waste product exchanging process. Therefore, the buffering function of aorta and large arteries is essential for smoothing out the pulsatility called “Windkessel mechanism” (Section 3.1) which provided by an expansion of elastic artery to accommodate the change of blood volume called arterial compliance. Windkessel mechanism is commonly observed in major arteries entire the body including intracranial space. However, unique characteristic of the intracranial space has fixed volume within rigid cranium. Also, the volume of four major intracranial contents (brain, arterial blood, venous blood and CSF) interact within this enclosed cranial cavity based on Monro-Kellie doctrine (Section 3.2). Hence, Windkessel mechanism of intracranial system provided by its arterial compliance and additional elastic properties of intra- and extracranial contents called intracranial compliance (Section 3.3). In healthy individuals, intracranial pressure (ICP) is distributed uniformly over entire intracranial space with bilaterally balance of cerebral blood flow (CBF). In contrast, the interhemispheric ICP gradients (Section 3.4) and asymmetry of CBF between two hemispheres (Section 3.5) are observed under pathological conditions.

38 3.1 Windkessel Mechanism and Pulsatility

Windkessel is the German word for air-chamber was first introduced as mathematical model by Otto Frank (German physiologist) to describe the hemodynamics in elastic arterial system [53]. As the Windkessel present in an old-fashioned fire engines (Fig- ure 3.1), water is pumped intermittently into an air-and water-filled chamber. Then, an air compressibility converts the pulsatile inflow of water into steady outflow at the hose nozzle while leaving the chamber. Likewise the cardiovascular system, blood pulsation created by the heart’s pumping action flows through the expansion and contraction of the elastic major arteries which act as buffering chambers. Blood then flows from the major arteries into smaller diameter vessels with intrinsic obstructive force then with continuous and pulseless outflow. Two main parameters describing Windkessel mechanism of arterial system are its elasticity of artery referred to “arterial compliance” and obstruction of blood flow from large artery to smaller artery referred to “peripheral resistance”.

Pump Chamber Nozzle

Heart Elastic Artery Peripheral Resistance

Figure 3.1: The concept of Windkessel mechanism. The air reservoir (chamber) is the actual Windkessel, and the large arteries act as the Windkessel. The combination of compliance, together with aortic valves and peripheral resistance, results in a rather constant peripheral ﬂow [189]

39 The arterial compliance plays an important role in absorbing and releasing energy during systolic and diastolic period. During systole, heart discharge the entire stroke volume of blood in form of kinetic energy into the arterial system. Approximately 50% of blood volume from cardiac contraction is dissipated forward to peripheral circulation, while remainder is stored as potential energy in the arterial vessel [16]. The storage of the remainder blood volume is provided by the role of peripheral resistance and elastic expansion of arterial wall by increasing arterial blood pressure. During diastole when arterial pressure falls, this elastic artery passively recoils and forces the storage volume into peripheral circulation by reconverting the stored potential energy during systole into kinetic energy [16]. Thus, this effective Windkessel function which act as hydraulic filter can convert pulsatile blood flow into nearly continuous peripheral flow by buffering function of elastic artery. In capillaries, this elastic properties of artery can also protect the damaging force from pulsatile flow in absorbing process between capillaries and cells.

Figure 3.2: Pressure-dependent arterial compliance [103]

The arterial compliance is deﬁned as the change in volume stored per change in internal pressure (Compliance = ∆V olume/∆Pressure) which is not constant but depends on the blood pressure with nonlinear relationship [77] as shown in Figure 3.2. Arteries with high compliance can accommodate large amount of blood with only

40 small increase in systolic pressure, therefore pulse pressure is in small range which reflects low aortic wall tension and heart work load [77]. Conversely, aging is usually much involved in loss of arterial elasticity which lead to reduced arterial compliance and increased pulse wave velocity [41]. In youth with high arterial elasticity, the forward-traveling wave (incident wave) transmission which generate and travel away from heart during systole is slow, thus during diastole its reflected wave returns from peripheral sites to the heart distally. In elderly with low arterial elasticity, the forward-traveling wave transmission is fast, thus its reflected wave returns to heart much earlier which allows the reflected wave to merge with the forward systolic wave [130]. As shown in Figure 3.3, in the elderly, the combination of the reflected wave which shifts from early diastole to late diastole and the forward systolic wave result in increased systolic pressure augmentation and decreased diastolic pressure, hence also increased central pulse pressure [41]. Consequently, high systolic blood pressure will increase the velocity of systolic blood flow by harder work of the heart’s left ventricle to eject blood to aorta [16] because noncompliant aorta cannot accommodate the cardiac stroke volume [77]. Thus, the normal cushioning function of Windkessel mechanism not only maintains the blood supply continuous throughout the body during diastole, when the heart is refilling and preparing for the next systolic contraction, but also reduces the cardiac afterload. Blood vessel tissue is mainly composed of smooth muscle, the highly elastic bundle of protein called elastin and very stiff protein in connective tissue called collagen [190]. As mentioned, the elastic properties of arteries, usually determined by smooth muscle and elastin [190] is diminished when the arterial stiffness increases due to the course of aging [16]. The stiffness of artery increase with aging results from the gradual loss of its elastic fibers with gradual replacement by collagen fibers [7]. Furthermore, there are other variables influence arterial elastic properties including gender [25, 96, 98, 104] and pathophysiologic conditions. Most of pathophysiologic conditions affect large arterial elastic properties [41] especially the aorta [16] and its first branches [172]. Under pathophysiologic conditions such as hypertension [17,

41 Figure 3.3: Central pressure contours and aging. The observed central pressure contours (upper tracings) are the sum (lower tracings) of the incident or forward-traveling wave (broken lines) and the reflected or backward-traveling wave (dotted lines). In younger subjects (right panel), the reflected wave (arrow) returns to the aortic root during diastole. As vessels get stiffer during the aging process (left panel), pulse wave velocity increases and the reflected wave returns during late systole (arrow), where it summates with the forward systolic wave to augment central systolic pressure and increase ventricular afterload [77]. (Adapted from Asmar R. Arterial Stiffness. 1999. [4])

76], hypercholesterolemia [99, 100] and atherosclerosis [42, 97], Windkessel buffering function is demolished which result from the large arterial wall stiffening due to the change in vascular structure including wall thickness and lumen diameter [190]. Arterial wall stiffening will reduce arterial compliance, increase pulse wave velocity and importantly widen pulse pressure. The widening of pulse pressure may induce additional decay of the arterial wall, then accelerate the loss of elastin [190]. For intracranial system, the cerebral blood flow through intracranial cavity has a unique characteristics which are different from any other part of the body because they are enclosed within rigid container for the purpose of brain protection. To maintain the normal cerebral blood flow and to ensure pulseless flow through cerebral capillaries, the effective intracranial pulsation absorber is required. During systole,

42 pulsatile arterial blood flow into the cranial cavity. The pulsatile energy from systolic arterial flow is transmitted and dissipated in the surrounding intracranial contents including CSF, elastic intracranial veins and subarachnoid space (SAS) which act as intracranial pulsation absorber. For example, since vanous blood and CSF connected to lower pressure region outside the cranium, the systolic expansion of cerebral arteries expulses the venous blood into the dural venous sinuses by compressing the venous outlets of the bridging vein [66]. Moreover, due to the spinal region (refers to spinal thecal sac) has higher compliance than the intracranial SAS during systole (and vice versa during diastole) [133], the pulsatile displacement of CSF downwards and upwards between cranium and spinal SAS through the foramen magnum [66, 84] to maintain the constant amount of volume within rigid cranium according to Monro- Kellie doctrine is the example of volume compensation mechanism to response to the systolic expansion of cerebral arteries. In addition, appropriate resistance of arteriole and capillary also must be provided to smooth out pulsatile arterial flow to non- pulsatile cerebral capillary flow for the effective nutrient exchanging process. The combination of intracranial Windkessel mechanism is essential for the maintenance of normal cerebral blood flow and a constant cerebral perfusion pressure [84]. The interruption of intracranial contents, for example, from the external force such as brain injury or intracranial disorder such as hydrocephalus can breakdown the intracranial Windkessel mechanism due to decreased intracranial compliance. The breakdown of the intracranial Windkessel mechanism results in increased intracranial CSF pulse pressure, restriction of arterial expansion, causing increased arterial resistance and reduced cerebral blood flow [46, 47, 61]. The restriction of arterial expansion will transmit outflow with high pulsatility to capillary which this pulse energy is ab- sorbed in the capillary instead of the artery [66]. Then, this systolic pressure pulse transmits from capillary to brain tissue and increases brain tissue pressure which decreases cerebral perfusion [66]. Also, the decreased intracranial compliance affects the autoregulatory mechanism of artery to maintain the normal level of cerebral blood flow [62].

43 3.2 Monro-Kellie Doctrine

The central nervous system is composed of incompressible intracranial contents which covered within a rigid container of skull. Variation in any of its intracranial content’s volume, the volume of the other contents will be compensated. To describe this complex compensatory situation, the principle of homeostatic intracerebral volume mechanism [82] was originally introduced in 1783 by Alexander Monro, a Scottish professor of anatomy. Monro [125] considered the cranium as a rigid structure of bone and only two intracranial contents (nearly incompressible brain and the volume of incompressible blood) interplay within this closed cranial cavity. Since the brain is nearly incompressible, the volume of blood circulating in the cranium is constant at all times which is a continuous outflow from the cranium of venous blood is compensated by a continuous inflow of arterial blood [124]. George Kellie [81], a former Monro’s pupil, supported Monro’s original hypothesis by his experiments and published in 1824. Based on animal experimentations, Kellie verified Monro’s hypothesis by considering three intracranial contents, i.e arterial blood, venous blood and brain tissue. He also stated that the removal of any circulating fluid from the cranium was not required simultaneous equivalent replacement; or the additional of any circulating fluid into the cranium was not required simultaneous equivalent displacement. In this literature, many Kellie’s observations agree with John Abercrombies’s literature which published before Kellie’s, and thus the term Monro-Abercrombie doctrine was found in Kelle’s literature [105]. In Abercrombie’s monograph [1] in 1828, Abercrombie strongly supported Monro’s and Kellie’s hypothesis based on his animal observations [105] and then their doctrine became widely accepted [185]. Although CSF was discovered before Monro’s publication [185] and CSF intraventricular flow through foramen was described and bound his name referred to foramen of Monro [105]. Monro obviously ignored the existence of CSF as a normal intracranial content [105]. The role of CSF in the cranium was first ignited by Francois Magendie in 1825. Magendie [108] proposed the flow of CSF from the fourth ventricle to the

44 subarachnoid space via the pathway of foramen which bears his name (foramen of Magendie). The revised version of the Monro-Kellie doctrine by accounting the volume of CSF into this equation of conservation of volume within rigid cranium was introduced by George Burrows in 1846. Burrows [24] observed replacement of blood lost due to systemic hemorrhage by CSF volume [185]. According to his experiments, the reciprocal relationship between volume of CSF and cerebral blood can be inferred. Finally, Monro-Kellie doctrine became known as the total volume within rigid cranium; the summation of the volume of brain tissue, arterial blood, venous blood and CSF, remain constant. A change in either content had to be compensated by the remainders.

Figure 3.4: Diagram showing the phase relationships of intracranial volume change measured by using ﬂow-sensitive MRI in (a) normal individuals and (b) patients with hydrocephalus. The curve of the volume changes in the artery is constructed as the inverse to the sum of the changes in the veins and intracranial CSF. In normal individuals, the expansion in the precapillary vessels is assumed to be somewhat larger than the corresponding compression on the venous side in order to correspond with the small brain expansion. In patients with hydrocephalus, the arterial is small as reﬂected in the small volume changes in the veins and in the intracranial CSF. As a result of the small arterial pulsations in SAS the pulse wave penetrates into compliant less distended intracerebral vessels resulting in a decreased intrinsic redistribution and large brain expansion [61].

The development of magnetic resonance imaging (MRI) technique in the past decade brings about the explanation of intracranial dynamics and volume compen-

45 satory mechanism within cranial cavity to describe the relationship between pulsatile flow of blood and CSF during cardiac cycle. Greitz et al. [61, 63, 65, 66] studied pulsatile motion of intracranial contents by using MRI technique. According to Monro-Kellie doctrine, the intracranial dynamics are related to the demand for volume by four intracranial contents, i.e. the arterial blood, brain volume, venous blood and CSF [65]. During systole, the expansion of carotid and basilar arteries in the closed cranial cavity [63] plays an important role in the dynamics and variation of intracranial volume which represented in Figure 3.4. The change of the arterial volume is inversely proportional to the summation of change in venous and intracranial CSF volume which mean the expulsion of the CSF and compression of veins are almost identical [61]. As shown in Figure 3.5, this systolic arterial expansion simultaneously dissipates the pulsatile energy to entire subarachnoid space which causes a compression of intracranial vein and expulsion of the extraventricular CSF upward to the intracranial subarachnoid space and downward to compliant spinal subarachnoid space (thacal sac) through the foramen magnum. During mid-systole, the less pulsatile and delay of arterial pulse wave outflow due to energy absorbing function of Windkessel mechanism is transmitted to the brain capillaries lead to small dilation of capillary and then cause brain parenchymal expansion [61]. Brian expansion, typically very small in the healthy individuals (about 2% of the arterial expansion [66]), leads to the compression of the brain ventricles (mainly on the lateral ventricles) which occurs simultaneously with an inflow of CSF towards the ventricular system to drive out the intraventricular flow of CSF [65]. During diastole, the higher pressure in spinal cavity result in flowback of CSF from spinal cavity into the cranial cavity. Thus, CSF repeatedly flow upward and downward between cranial and spinal cavity during the entire cardiac cycle. Nowadays, Monro-Kellie doctrine is essential for many clinical applications i.e. to explain the failure of volume compensatory mechanisms due to space occupying lesion such as hematoma in patient with traumatic brain injury (TBI) which often develop intracranial hypertension [82]. Also, CSF volume depletion caused by CSF leakage or

46 Figure 3.5: Normal intracranial hydrodynamics. The relative thickness of the arrows in the artery (red) indicates the magnitude of pressure. The relative thickness of the arrows in the venous system (blue) and subarachnoid space indicates the magnitude of ﬂow [162]. (Modiﬁed from Greitz [66])

CSF over-drainage during shunt placement which require volume compensation can be explained by Monro-Kellie doctrine [124].

3.3 Intracranial Compliance

To smooth out arterial pulsatile flow into a continuous and steady flow through peripheral tissue within the cranium, the effective intracranial Windkessel mechanism which depends on a storage capacity of both vascular compliance and compliance of CSF space are required. These combination of volume compensatory mechanism act as pulsation absorber in intracranial system called intracranial compliance. Thus, overall intracranial compliance depends on the compliance of four main intracranial contents [178]: brain tissue (typically is small in healthy individual [61]), arteries, veins (very high compliant venous wall [69, 78]) and spinal thacal sac (located in lumber space which buffer CSF pulsatile flow from cranial cavity during systolic expansion of intracranial arteries [66]). In addition, the elastic property of other intra- and extracranial contents (i.e. ependyma, dura mater, intracranial and spinal subarachnoid space) is another factor that affects intracranial compliance. Intracranial compliance is defined by the change in CSF volume per unit change in intracranial pressure (C = dV/dPICP ).

47 Figure 3.6: Illustration of the ICP-volume curve and its relationship to the intracranial pulsatility parameters. Under normal physiological conditions with high intracranial compliance, the ICP wave amplitude is correspondingly small. As intracranial compliance decreases (steep part of the pressure-volume curve), the brain behaves increasingly like a linear elastance and so variations in intracranial volume correlate increasingly well with changes in mean ICP, the steepness of the pressure-volume curve also accounts for large-amplitude ICP waveforms [48].

Based on the experimental observation, Marmarou et al. [112, 113] invasively measured intracranial compliance by injecting known ﬂuid volumes via a balloon insertion into the CSF space to analyze the ICP response to changes in CSF volume. They found that the intracranial compliance decreased as mean ICP increased exponentially along a pressure-volume curve as presented in Figure 3.6. The pressure-volume curve describes the relationship of ICP pulse pressure and volume by the amplitude of ICP pulse pressure increase with exponentially rise of mean ICP. Also, the exponential pressure-volume curve can be used to explain the eﬀectiveness of volume compensatory mechanism in the cranium. At normal ICP levels, the large increase in intracranial volume causes a small increase in mean ICP and only small change in ICP pulse pressure which indicates good intracranial compensatory reserve. Conversely,

48 while the mean ICP is elevated, the intracranial volume compensatory capacity becomes exhausted progressively. Only small increase in volume results in the larger in the amplitude of ICP pulse.

(a) (b)

Figure 3.7: (a) The CSF volume-pressure curve (b) The same data plotted on semilogarithmic axis can be approximated by a straight line which its slope is equal to the pressure-volume index (PVI) [113].

As shown in Figure 3.7, the exponential pressure-volume curve can be simplified to linear approximation slope by plotting the logarithm of the pressure against the volume change which is defined as pressure-volume index (PVI). The PVI is defined as the amount of fluid volume (∆V ) necessary to raise pressure by a factor of 10 and can be calculated from the relationship [112, 113]:

∆V PVI = log P 10 P0 where P0 and P are initial and peak pressure level respectively. The PVI can be used for calculation from the standard clinical method to determine intracranial compliance known as “bolus injection” by injecting the amount of ﬂuid volume in the spinal subarachnoid space required to achieve a tenfold increase in ICP and record the pressure rise. Also, the PVI can be used to access the CSF dynamic and identify the neurosurgical patients with exhausted intracranial volume

49 compensatory capacity such as traumatic brain injury (TBI) [114] and hydrocephalus [145, 150] by comparing to the reference. For normal adult, a mean PVI of 25.9 ml, a mean ICP of 13.2 mmHg and a mean intracranial compliance of 0.85 ml/mmHg were used as clinical references [151]. The measurement of intracranial compliance plays an important role in clinical diagnosis or treatment the pathological conditions related to intracranial compliance changes such as hydrocephalus and TBI. However, direct measurement of intracranial compliance is technically diﬃcult [178] and not practically performed because the pressure-volume response test might increase the risk of patients who already load with intracranial space occupation [164]. Typically, most investigators have used the intracranial pulsatility as an indicator of the change in intracranial compliance. Three primary measuring techniques have been used for assessment of intracranial pulsatility: continuous ICP monitoring, transcranial Doppler ultrasound (TCD), and magnetic resonance imaging (MRI) [178]. ICP monitoring is invasive measurement of pressure pulsatility to assess the dynamics and pulse amplitude of intracranial pressure either in the time domain or the frequency domain. As described above in the exponential pressure-volume relationship, intracranial compliance is reduced with increased mean ICP which result in larger amplitude of CSF pulse pressure along the curve. Hence, the amplitude of CSF pulse pressure in the time domain (i.e. diastole-to-systole ICP diﬀerence over one cardiac cycle) can be clinically used as an indicator of intracranial compliance [5, 6]. However, some observation in the patient with pathological conditions such as SAH [48] and hydrocephalus [52], Eide et al. [48] observed that the relationship between mean ICP and amplitude of CSF pulse pressure along the curve has good correlation only 60% of observations. Also, Foltz et al. [52] observed an increase in amplitude of CSF pulse pressure with reduced mean ICP in some patients. These observations may imply that the correlation of mean and its amplitude pulse is more complicated to explain by the predicted pressure-volume curve [48] because reduced intracranial compliance may not necessarily lead to higher mean ICP or ICP pulse

50 Figure 3.8: Schematic depiction of the pressure-volume compensation index (RAP) theory [83]. pressure [178]. For analyzing pressure pulsatility in the frequency domain, the ICP waveform consists of three overlapping components in the time domain which can be separated in the frequency domain by using the fast Fourier transform [34]. Czosnyka et al. studied the amplitude of fundamental frequency component (AMP) [37] which is the harmonic component of ICP pulse waveform that has a frequency equal to the heart rate [34]. Thus, AMP is the amplitude of the fundamental harmonic frequency component of the ICP pulse waveform derived from the Fourier decomposition with a reasonably time period window [83]. Interestingly, AMP has a good correlation to mean ICP and the degree of this correlation over short periods of time can be expressed as an index of pressure-volume compensatory reserve (RAP) [34, 37]. RAP

51 index can be calculated as a linear correlation coefficient between AMP and mean ICP from a reasonably time period (usually 6-10 s) and data points (usually 40 data points) [34]. As shown in Figure 3.8, the pressure-volume curve (Figure 3.8 (A)) can be mainly divided into 3 regions. In region I, RAP coefficient (Figure 3.8 (C)) close to 0 indicates less correlation between the changes in AMP and the mean ICP (Figure 3.8 (B)). This linear relationship between volume and pressure in region I implies a good compensatory reserve at low ICP where change in volume is independent of mean ICP [34]. In region II, exponentially rise in ICP with increase in volume along pressure-volume curve indicates decrease of intracranial compliance and exhaustion of capacity to compensate for change in intracerebral volume [38]. AMP directly increase with mean ICP, consequently RAP usually rises to +1 to response to a poor compensatory reserve in region II [83]. In region III, passively compression of cerebral arterioles [34] and then decrease in transmission of arterial pulse pressure to intracranial space result from impairment of active cerebrovascular regulatory mechanisms which can be developed to the brain ischemia [83]. Critically rise in ICP toward the right in pressure-volume curve bring about decrease in AMP and below 0 in RAP level. RAP index is useful for diagnostic purposes in patients with intracranial pathology; for example, to distinguish chance of recovery for head injured patients [32] and to diagnosis hydrocephalus in children [147]. Because ICP monitoring is invasive technique, it can simultaneously monitor and compare the pulse pressure wave in different intracranial regions which is the advantage of invasive technique over non-invasive measuring techniques [178]. Transcranial Doppler ultrasound (TCD) is non-invasive technique to measure blood flow velocity through major intracranial arteries which commonly performed on the middle cerebral artery (MCA). The output of a TCD measurement is a flow velocity waveform in the time domain for typically many cardiac cycle of monitoring period [178]. This flow velocity waveform obtained from TCD provides an important cerebral hemodynamics information called pulsatility index (PI) which describes the velocity pulsatility of intracranial artery [44]. Based on Gosling’s method [59], PI is commonly

52 expressed as (peak systolic flow velocity - peak diastolic flow velocity)/mean velocity. Because PI (flow velocity) depends on many intracranial hemodynamics factors, a good correlation between PI and various intracranial parameters including arterial pressure pulsatitily, ICP [15, 73, 128, 141], cerebrovascular resistance (CVR) [36, 56], cerebral perfusion pressure (CPP) [33, 126, 170] as shown in Figure 3.9 can be used for clinical assessment. However, measuring only blood flow velocity, not volumetric flow due to unknown of vascular diameter is the common technical limitation of TCD investigations [15]. Frequently, decreased intracranial compliance is associated with increase in PI because PI is a ratio absolute pulsatility and mean velocity [178]. Since PI depends on both pulsatility and mean flow velocity, increase in PI may result from decreased cerebral mean velocity due to lower blood flow rather than an increase in absolute pulsatility [178]. Thus, PI cannot interpret entire intracranial physiological condition individually, other information is required to support this complex function of various interdependent dynamics for clinical diagnostic accuracy [44].

Figure 3.9: Timetrends of intracranial pressure (ICP), arterial blood pressure (ABP), cerebral perfusion pressure (CPP), mean cerebral blood ﬂow velocity (FVm), pulsatility index (PI) and cerebrovascular resistance (CVR) in patient with head-injury [44].

Magnetic resonance imaging (MRI) is also non-invasive ﬂow-based method for measurement of intracranial blood ﬂow (within large intracranial arteries or veins)

53 and CSF flow (within CSF circulatory pathways) collected over many cardiac cycles [178]. The output of MRI measurement, one cardiac cycle waveform which represents an average resultant over many cardiac cycles’ dataset, can be both two-dimensional (flow velocity waveform) and three-dimensional image (volumetric flow) which is MRI- specific advantage over TCD technique [178]. As described in the previous section, the volumetric relationship between intracranial blood and CSF pulsatile flow during cardiac cycle can be investigated by MRI method which provide an essential information for assessment of intracranial compliance. The intracranial compliance can be estimated by using either direct or indirect approach [164]. For direct approach, the intracranial compliance is directly calculated from the ratio of the change in the intracranial volume and pressure during the cardiac cycle according to the definition of compliance. The intracranial volume change (net transcranial volumetric flow rate) is the differences between volume of fluid (blood and CSF) inflow to and outflow of the cranium during the cardiac cycle [2, 164]. The intracranial volume change include the total volumetric arterial inflow rate, the total volumetric venous outflow rate, and the CSF of outflow rate through the foramen magnum with the constraint of volume conservation based on Monro-Kellie doctrine [2, 164]. The volumetric flow rates are obtained from integration of the velocity waveform within blood vessel and CSF lumen with respect to time [164]. The total volumetric arterial inflow rate (total cerebral blood flow) is the summation of the volumetric flow through four major arteries supplying blood to the brain including bilateral internal carotid arteries and vertebral arteries [2]. The total volumetric venous outflow rate is the summation of the outflow through the jugular veins and secondary veins including epidural, vertebral and deep cervical veins [2]. The intracranial pressure gradient waveforms are approximately derived from a time derivative of the CSF flow velocity waveform based on the Navier-Stokes relationship between pressure gradient and temporal-spatial derivatives of the fluid velocity for incompressible fluid in a rigid tube [2, 164] which the measuring method for pulsatile pressure gradients by using MRI was proposed by Urchuk and Plewes [169].

54 (a) (b) (c)

Figure 3.10: (a) Arterial and venous flow in the superior sigital sinus (SSS) territory in a healthy patient. (b) In NPH patient, arterial and venous flows are almost identical shape with minimal delay. The mean volumetric blood flow through SSS in NPH patients is 27% lower than in the healthy individuals. (c) After shunting (removal of 30 mL of CSF), the arterial flow has earlier, higher, and thinner peak. The venous flow peaks later, is lower, and wider. Modified from Bateman [11].

For indirect approach, since the intracranial compliance has influence on the timing or phase-lag of flow and pressure waveforms entering the cranium which have a unique morphology, it is the useful indicator to analyze the intracranial compliance and its abnormality [178]. The phage-lag method [164] focuses on the phase shift or relative timing between arterial flow or pressure waveform (typically used as reference waveform because intracranial pulsation is generated by arterial blood flow [178]) and other intracranial waveforms such as CSF flow [8, 9, 46, 177], ICP and venous outflow [11, 13]. For example, Baledent et al. [9] found the smaller phase

55 shift between the systolic peak of arterial inflow and cervical CSF flow in hydrocephalic patients compared to healthy individuals. In addition, Bateman [11] showed the shorter delay between arterial inflow and venous outflow systolic peaks in NPH patients, while venous peak became lower and longer delay after surgical shunting as shown in Figure 3.10. In the studies of intracranial compliance by using either MRI-based or model-based investigators, there are other aspects also can be used as the estimator of intracranial compliance such as shape of ICP waveform, CSF flow rate, and amplitude of intracranial waveform. The transformation of peaks and dips characteristic pattern [178] along systolic and diastolic cardiac cycle of ICP waveform have been observed in the patients with hydrocephalus [74] and/or elevated ICP [165, 179] by smoothing out their characteristic features. Based on MRI data of CSF flow through cerebral aqueduct (connect between the third ventricle and the fourth ventricle), many investigators have been reported a significant increase in CSF pul- stile flow rate through cerebral aqueduct under hydrocephalic conditions [14, 61, 176]. In the studies of change in pulsatility of vascular flow in NPH patients [11, 12, 14], the decrease in arterial flow pulsation and change in venous pulse wave have been observed in NPH patients (Figure 3.10). Based on model approach, the amplitude of the ICP pulse wave increase with pathological conditions such as hydrocephalus have been proposed [138, 139, 140]. In summary, intracranial compliance is associated with the intracranial volume compensatory mechanism which is illustrated by an exponential pressure-volume curve (Figure 3.6). In patients with neurological conditions such as hydrocephalus or TBI, the development of intracranial space occupation within the closed cranium based on Monro-Kellie doctrine may exhaust its compensatory mechanism which is the indication of reduced intracranial compliance. Moreover, the exhaustion of volume compensatory mechanism can cause the change in intracranial pulsatility (i.e. amplitude, waveform, velocity, flow rate, timing, etc.) in various aspects including ICP, blood and CSF flow dynamics which can be observed by using many different measuring techniques such as ICP monitoring, transcranial doppler ultrasound (TCD)

56 and magnetic resonance imaging (MRI). Hence, the assessment of intracranial compliance by measuring the intracranial pulsatility brings about the valuable information of intracranial compliance’s role for clinical diagnosis and decision making.

3.4 Interhemispheric Pressure Gradients

Based on Monro-Kellie doctrine, cranium is generally considered as a single rigid compartment with uniform distribution of intracranial pressure (ICP) over entire intracranial space [39]. However, there are many experimental studies in animal and clinical reports in head-injured patients associated with differences in ICP between intracranial tissues [137] and between left and right cerebral hemispheres. For experimental observation, researchers used various techniques to induce elevated ICP and monitor the interhemispheric ICP gradients such as intracranial balloon expansion, fluid injections and stroke. In 1885, von Bergmann’s experimental studies [174] demonstrated the first existence of intercompartmental pressure difference and concluded that the brain does not transmit pressure equally in all directions. In 1902, Cushing [31] described an unequal transmission of intracranial pressure throughout the intracranial space and regional differences in cerebrovascular response resulted from “local compression” experimentally produced by mercury-filled rubber bag expansion in subdural space. Langfitt et al. [92, 94] demonstrated unequally transmission of pressure between left and right cerebral hemispheres by injecting saline into monkey’s extradural space. Also, the authors found that a failure of pressure communication from the supratentorial to the infratentorial space occur as cerebral tissue obstruct the tentorial in- cisura [94]. Furthermore, the transmission of increased intracranial pressure within the supratentorial space were experimentally designed by inserting a balloon with saline into the frontal lobe and injecting Pantopaque into the extradural space via a catheter. This experimental observations had shown the higher ICP in the fluid- injected side but lower and slightly lag of contralateral ICP followed the injected side

57 in most case. The brain herniation was also observed in animal with markedly elevated ICP. The authors summarized that the failure transmission of increased ICP due to mass lesion resulted from the distensibility limitation of the brain and the intracranial tissues. However, without subarachnoid space obstruction, subarachnoidal pressure was transmitted freely over the cerebral hemisphere [92]. Brock et al. [20] reported ICP gradients associated with cerebral embolism by injecting an oil emulsion through the right lingual artery catheter to create unilateral oil embolism of the cerebral blood vessel or vascular occlusion in a series of 20 cats. All animals died eventually following the oil injection and categorized into 3 groups depended on the survival time. The result (Figure 3.11) showed that the higher epidural pressure of non-embolized hemisphere and larger interhemispheric pressured differences between two cerebral hemispheres existed in 12 cats following oil injection. This might be due to large vascular blockage of embolized side. Higher epidural pressure would be either on the embolized or non-embolized side, the authors stated, “... may be related to the degree of vascular occlusion achieved or to the distribution pattern of oil emboli” [20]. Reulen and Kreysch [143] performed cold lesion experiment and recorded brain tissue pressure in 15 cats by using wick probe. A cold injury induced the highest pressure in the adjacent to the lesion and followed by remote from the lesion, cisternal fluid pressure and on the non-lesion side respectively. Also, the pressure gradients from each recorded position became larger when the hypercapnia was observed. By using wick-type pressure transducers, Tulleken et al. [167] recorded regional cerebral tissue pressure under 4 different experimental conditions in 31 animals (14 cats, 7 macaques and 10 baboons). The injection of Pantopaque in the middle cerebral artery and in the common carotid artery, represented a localized rapidly intracerebral volume or infarction by vascular occlusion, resulted in marked degree of interhemispheric ICP gradients (Figure 3.12). In addition, the rapid inflation of a subdural or epidural balloon, represented a rapidly growing extracerebral volume, resulted in moderate degree of interhemispheric ICP gradients (Figure 3.13).

58 Figure 3.11: Mean values of epidural pressure on the right (PR) and left (PL) sides in various groups of animals. Oil embolization always performed on the right side. All pressures are positive. The animals in which epidural pressure increase was more pronounced on the right (embolized) side were inscribed above the x-axis. The animals which epidural pressure increase was more pronounced on the left (non-embolized) side were inscribed below x-axis. Interhemispheric pressure gradients were more pronounced when epidural pressure increased more on the non-embolized (left) side. [20]

Significant interhemispheric ICP gradient ranging from 5 to 14 mmHg was observed from Miller et al. ’s experimental model [121]. After subdural balloon inflation and intracerebral silicone injection in cats and rhesus monkeys, the authors observed that “the pressure being greatest in the ipsilateral hemisphere and lowest in the contralateral hemisphere” [121]. Wolfla et al. [195] measured the regional intraparenchymal pressure in 5 locations including the right (RF) and left (LF) frontal lobes, the right (RT) and left (LT) temporal lobes, the midbrain (MB) and the cerebellum (CB). A balloon catheter was inserted into the right frontal epidural space (RF) and expanded by saline injection to create a frontal epidural space mass lesion in 10 domestic pigs. The experimental results showed “the pressure differentials between intracranial regions increased as the size of the mass increased” [195]. Also, a consistent relationship between the

59 Figure 3.12: Injection of Pantopaque into right middle cerebral artery of cat [167] intracranial regions was RF >LF >RT=LT >MB >CB. In this study, the authors also stated that “...if a gradient forms, the highest tissue pressures would occur closest to a mass lesion” [195]. Moreover, the authors conducted similar experiment to previous report in the following year. In this study [194], an extradural temporal mass lesion was created by balloon expansion in the right temporal lope (RT). The pressure relationship after the balloon expansion was RT >LF=LT >RF >MB >CB. The authors concluded that the presence of pressure gradients depended on, not only lesion size, but also the mass location [194]. In clinical case report, Weaver et al. [184] reported 4 of 20 patients with most clearly interhemispheric ICP gradients by using bilateral subarachnoidal pressure catheters due to mass lesions including temporal tip contusion, internal capsule hemorrhage, frontoparietal subdural hematoma and temporal tip hematoma. The authors also stated that “more than 50% of the 20 patients evaluated demonstrated signiﬁcant diﬀerential ICP’s at sometime during their period of continuous monitoring” [184]. Chambers et al. [27] monitored ICP bilaterally in 10 severe head-injured patients (5 contusions, 2 intracerebral hematoma (ICH), and 3 subdural hematoma (SDH)). In

60 Figure 3.13: Alternating inflation of two balloons over left and right hemisphere of baboon [167] patients with subdural hematoma (SDH) as presented in Figure 3.14(a), the reading showed the positive interhemispheric ICP gradients (ipsilateral-contralateral) which mean ipsilateral side has higher ICP than contralateral side. However, the recording in patients with contusions and ICH (Figure 3.14(b)) showed both positive and negative interhemispheric ICP gradients. Hence, this observation might imply that the higher ICP side would either on the ipsilatheral or contralateral side might depend on the severity of head injury and appearance of mass lesion. Sahuquillo et al. [144] have observed the interhemispheric supratentorial ICP gradients in 50 head-injured patients. According to CT scanning criteria, each patient was categorized into one of three groups depend on the size of mass lesion and midline shift. In addition, the recorded supratentorial ICP pattern was classified into 4 patterns: Pattern I a difference of mean ICP (<3 mmHg) and global ICP amplitude (<2 mmHg) were very small so the intracranial compartment can be considered as a unicameral space, Pattern II, III and IV the ICP recording was showed clearly interhemispheric pressure gradients with larger difference of mean ICP (>3 mmHg) and global ICP amplitude (>2 mmHg). The summary of types of lesions according to CT scan and ICP pattern table (Table 3.1) showed that the head-injured patients with mass lesion size larger than 25 ml (Focal A) and with midline shift greater than 3 mm

61 (a) (b)

Figure 3.14: Diﬀerence between ipsilateral and contralateral ICP recording from patients with (a) subdural hematoma and (b) contusions or intracerebral hematoma [27]

(Focal B) had more chance to observe the interhemispheric ICP gradients than the patient with small mass lesion (<25 ml). In this study, the authors suggested that the interhemispheric ICP gradient be probably due to the partial blockage of cistern or the complete obstruction of the subarachnoid spaces.

Table 3.1: Summary of types of lesion according to CT scan and ICP pattern [144].

D’Ambrosio et al. [39] studied interhemispheric ICP gradients in 7 adult male baboons with stroke. Each baboon was subjected to left focal cerebral ischemia/reperfusion

62 (I/R) injury by temporary ligation of the left internal carotid and bilateral anterior cerebral arteries. In this study, animals with large infarct volume (>20%), the ipsilateral ICP was higher than the contralateral ICP with a mean pressure gradient of 13.8 ± 4.3 mmHg. However, the contralateral ICP was higher than the ipsilateral ICP with a mean ICP gradient of 2.6 ± 1.1 mmHg for animals with ≤ 15% infarction volume as shown in Figure 3.15. The authors also stated that “This dichotomization of pressure gradients based on infarct size is likely due to multiple factors including the compliance of the intracranial tissues and the rate at which edema accumulates in cerebral ischemia” [39].

Figure 3.15: Interhemispheric ICP gradients and infarct volumes for all animals. Hourly interhemispheric ICP gradients (mmHg) are plotted over time. Percent ipsilateral hemispheric infarct volume is noted for each animal [39].

In many clinical cases recorded in patients with unilateral mass lesions, the significant diﬀerence between ipsilateral and contralateral ICP with the higher ICP in the lesion side were observed [54, 123, 182]. However, the existence of interhermispheric ICP gradients and inquality distribution of ICP in the intracranial space are still controversial clinical issue. For example, in the study of 15 head-injured patients with mass lesions, Yano et al. [198] observed contradictory results with no signiﬁcant interhemispheric ICP gradients throughout the supratentorial space. They concluded that “... the intracranial space, especially the supratentorial space, in one compartment in which pressure distribution is generally uniform” [198].

63 Various factors are involved in the confliction in interhemispheric ICP gradients observations. Basic anatomic difference between non-primate and primate model bring about conflicting experimental findings [39]. Intracranial anatomic structure of non-primate model are different from primate model, so the obtained results can not be compared directly. In addition, different location of monitor placement, measurement method and equipment can provide different experimental results. Many researchers suggest that ICP monitoring should be placed in both hemispheres to control ICP of patients with neurosurgical disorders. Possibly, the contralateral side may has higher ICP than the injured hemisphere. Furthermore, in the study of the relationship between interhemispheric ICP gradients, clinical signs and CT scans from 6 patients with severe head trauma, Mindermann and Gratzl [122] summarized that “ clinical signs and CT scans do not seem to predict reliably a lateralized ICP” [122]. In order to understand the unclear interhemispheric ICP gradients various physiological factors including CSF dynamical flow, cerebrovascular reactivity, elastic and plastic properties of brain tissue should be focused as well [184].

3.5 Eﬀect of Neurosurgical Disorders on Cerebral Blood Flow

Neurosurgical disorders such as hydrocephalus and TBI which may be secondary to intracranial hypertension can cause numerous effects on intracranial space including brain distortion, herniation of intracranial contents, blockage of CSF flow, and especially reduced cerebral blood flow. Reduced cerebral blood flow (CBF) further results in irreversible brain ischemia (CBF <18 ml/100 g/minute) and dysfunction of nervous system. There are two main factors related to reduced CBF. First, acute intracranial hypertention can cause the reduction of CBF. When ICP is increasing, CBF becomes progressively reduced because of decreased cerebral perfusion pressure. Then, CBF will stop eventually when ICP equals to the systolic arterial blood pressure [90]. Sec- ond, a space-occupying lesion also can increase ICP and produce the compression and

64 distortion of brain tissue. These effects are associated with the size of mass lesion and the rate of mass lesion expansion [91]. When the mass lesion expand beyond the intracranial volume compensatory capacity, the ICP will increase and then CBF will reduce due to the compression of cerebrovascular bed. The exhaustion of volume compensatory mechanism might be resulted from the blockage of CSF flow pathway which provide pressure communication to the posterior fossa and spinal canal [94]. The blockage of CSF flow pathway, caused by brain-stem compression produced by mass expansion, can build up ICP and herniation of cerebral tissue [94]. The studies of decreased global CBF and regional CBF were reported in the observation of animal testings and clinical case reports of the patients with traumatic brain injury (TBI) and hydrocephalus. Langfitt et al. [93] observed 28 rhesus monkeys with marked intracranial hypertension created by expansion of balloon in the right parieto-occipital subdural space. ICP, carotid arterial blood flow, sagittal sinus, jugular vein lumbar subarachnoid and systemic arterial pressure were recorded as shown in Figure 3.16. The authors found that the acute expansion of the extradural balloon resulted in increased ICP and reduced carotid arterial blood flow due to the reduction of the cerebrovascular bed diameter proximal to the sinus. Also, during the period of occlusion of common carotid artery, produced by balloon injection, the contralateral common carotid artery was ligated. Same group of researchers [149] conducted similar monkey’s experiment and morphologically demonstrated the compression of both the sagittal sinus and proximal vessels due to increased ICP. Major cerebral vessel and small arteries and veins in sulci were collapsed due to expansion of balloon or brain swelling. However, the other small vessels were unaffected. The authors also discussed about cerebrovascular collapse produced by brain swelling and intracranial hypertension. The thickness and diameter of vessel as well as the intravascular and extravascular blood pressure were the important factors for inducing or preventing cerebrovascular collapse. The study of cerebrovascular compression, the displacement and distortion of brain tissue in monkeys and cats, created by acute expansion of an extracerebral balloon,

65 Figure 3.16: Effect of acute expansion of the extradural balloon on carotid blood flow (BF), jugular vein pressure (Jug), intracranial pressure (ICP), sagittal sinus pressure (Sag), lumbar subarachnoid pressure (Lum) and systemic arterial pressure (SAP). Arrow indicate beginning and end of injection. Time between triangles one minute. In this and all subsequent illustrations pressures are indicated in mmHg and flow in ml/min. [93]. were observed by Weinstein et al. [186]. They found that rapid expansion of an extracerebral balloon lead to brain ischemia which caused by ceasing of cerebral blood flow for both adjacent and remote to the balloon. Also, the degree of displacement and distortion of various intracranial contents such as tentorium, inferior colliculus, occipital lope, corpus callosum, cerebellum, cerebellar tonsils and hypothalamus were related to the location, the function of volume and the rate of fluid-injection of the balloon. However,“ the pathological effects of diffuse intracranial hypertension were much less profound than those produced by rapidly expanding mass” [186] due to space availability for volume accommodation and the elasticity of brain tissue and intracranial contents. Johnston and Rowan [79] measured CBF and several intracranial site including ventricle, subdura, and cisterna magna in each cerebral hemisphere separately. El-

66 Figure 3.17: Mean right and left cerebral hemisphere blood flow levels, with increasing mean intraventricular pressure [79]. evated ICP was produced by expansion of balloon which placed in supratentorial subdura of the right cerebral hemisphere. They found that as ICP was progressively increased, the CBF for both hemispheres became lower as presented in Figure 3.17. Especially, the blood flow in the lesion hemisphere was consistently lower than that in the contralateral side. In this study, an intercompartmental pressure gradient between supratentorial and infratentorial pressure caused by balloon expansion was also monitored. By gradually expanding extradural balloon in the parieto-occipital zone of the right cerebral hemisphere in baboons, Symon et al. [163] studied the effect of supratentorial space-occupying lesions on intracranial pressure, CBF, pressure perfusion and the displacement and distortion of intracranial tissue. During gradually expanding balloon, resulted in an increased ICP, the supratentorial pressure of the inflated- balloon hemisphere is higher than the contralateral side, the interhemispheric supratentorial pressure gradients become larger and reducing of total CBF. Also, cerebral blood flow of lesion side is less than the contralateral side as shown in the comparison

67 table of blood ﬂow (Table 3.2). The authors explained the evidence of experimental observations resulted from the failure of autoregulatory capacity.

Table 3.2: Eﬀect of extradural expanding lesion on cerebral blood ﬂow [163].

In experimental brain injury induced by fluid-percussion model in animal, the reduction of global CBF was widely observed [45, 131, 168]. In the measurement of regional CBF after experimental TBI by inducing unilateral fluid-percussion brain injury in rat, Yamakami and McIntosh [197] found that 15 minutes after injury, significantly decreased global and regional CBF in all brain region as presented in Table 3.3. At 0.5 to 2 hour after injury, the most reduction of regional CBF was found in the injured site. CBF gradually recovered to near normal (pre-injury) level at 4 hour after injury. In addition, similar experiment and results were performed by Ozawa et al. [135] as illustrated in Figure 3.18. Moreover, the marked reduction of global CBF below normal levels typically found in patients with severe TBI [18, 19, 30, 49, 111, 132]. For regional CBF, the significantly lower CBF within [117] and adjacent [19, 117, 132] to the mass lesion than that global CBF virtually observed in the TBI case report. These findings also agreed with animal models [22, 120]. In measurements of CBF in 35 severe head-injured patients, Bouma et al. [19] found that the patients with acute intracranial hematomas had the

68 Table 3.3: Regional and total brain cerebral blood ﬂow in rats subjected to ﬂuid- percussion brain injury [197].

lower CBF on the ipsilateral hemisphere than the contralateral side. The most severe reduction was found in the the parietal and temporal region where the hematomas commonly observed as presented in Figure 3.19. The changes of regional CBF under various pathophysiological conditions caused by subarachnoid hemorrahage (SAH) in patients with ruptures intracranial aneurysms were studied by Ishii [75]. The author found that most patients with severe diffuse vasospasm (a constriction of a vascular lumen), or with large intracerebral hematoma, or with ventricular dilation (hydrocephalus) showed marked reduction of global and regional CBF. Further reduction of regional CBF in hematoma and vasospasm region when accompanied by venticular dilation was also observed. The author concluded that the degree of reduction in CBF correlated well with the clinical severity of neurological deficits and the relief of hematoma and ventricular dilation might improve CBF and consequently clinical outcomes [75]. In clinical case report of CBF in patients with normal pressure hydrocephalus (NPH) by using various measurement techniques, most researchers found significantly reduced global CBF in patients with NPH compared to normal individuals [21, 60, 67, 68, 72, 86, 88, 116, 118, 175]. Also, the reduction of regional CBF was reported with the most profound reduction in frontal region [60, 85, 107, 119, 134]. For cerebral

69 Figure 3.18: Changes in regional cerebral blood flow (rCBF) in the visual (A), parietal (B), sensorimotor (C), and frontal cortices (D) of the injured and the contralateral sides. rCBF decreased remarkably in the injured side following insult for 4 hours. After 24 hours, rCBF recovered except in the visual cortex. rCBF also decreased slightly in the non-injured side. Modified from Ozawa et al. [135]. blood flow improvement after surgical intervention, shunting can increase in CBF in many studies [21, 67, 68, 85, 86, 118, 119, 175]. However, in the study of 43 patients with communicating hydrocephalus secondary to subarachnoid hemorrhage (SAH), Hayashi et al. [72] found that shunting cannot improve CBF in the patients with mean CBF less than 25 ml/100 g/min. Moreover, no significant improvement of CBF after shunting was observed in some case reports [88, 109, 116, 127]. Because NPH was related to ventricular dilation, the relationship between decreased CBF and ventricular size was controversial issue [134]. Some observations found the correlation between reduction in CBF and size of ventricular dilation [67, 68, 72, 175]. However, no correlation was found in some reports [109, 116, 127] To maintain well neurological function, various factors related to cerebral vascula-

70 Figure 3.19: Graph showing ipsilateral and contralateral regional cerebral blood flow (CBF) values in measured areas in patients with intracranial hematomas. Regional CBF in parietal and temporal lobes was significantly lower on the side ipsilateral to the hematoma. Error bars indicate standard error of the mean. FR = frontal lobes; PA = parietal lobes; TE = temporal lobes; OCC = occipital lobes; BASG = basal ganglia; CBL = cerebellum; BS = brain stem [19]. ture and blood flow such as ICP, cerebral perfusion pressure (CPP), arterial distensibility and autoregulation should be controlled in normal level otherwise cerebral blood flow would be reduced and further intracranial contents would be distorted. Cere- brovascular collapse (vasospasm) was one of the most common effect to morbidity and mortality of the patients with TBI secondary to an expansion of mass lesion. This collapse occured when the intracranial tension beyond its limitation which caused the reduction of cerebral blood flow and further resulted in cerebral ischemia and infarction. A wide variation of anatomical lesions such as type, size and location of lesion is the factor that effect cerebral vasculature and blood flow [19, 111]. The studies of regional cerebral blood flow found that the cerebral blood flow of the injured side and adjacent to the lesion was typically lower than the contralateral hemisphere. Hence, these findings enhance that these vulnerable regions should be particularly considered in the treatment of head-injured patients.

71 Chapter 4

Review of Windkessel Model and the Model of Intracranial System

In this chapter, the model of intracranial system based on Windkessel mechanism will be reviewed which is divided into two sections. First, to describe the blood ﬂow and pressure through the major arterial system and electrical element provided by Windkessel model will be reviewed. Second, the intracranial system model focusing on the study of intracranial behavior based on two major types of model i.e. complex compartment and pulsatility models.

4.1 Review of Windkessel Model

A lumped parameter or one-dimensional model called Windkessel model was well- known tool to explain the hemodynamics through arterial system by using electrical element. The characteristic function of artery can be represented by the electrical element in the simple RLC circuit. For example, the ability to store the electric energy of capacitor (C) represents the ability to store the volume of blood by arterial elasticity or compliance. Also, the ability to reduce the electric energy of resistor (R) represents the resistance of blood ﬂow due to the change in vascular lumen or the length of artery. Windkessel model was ﬁrst introduced as mathematical model by Otto Frank [53]

72 in 1899. Frank formulated the hemodynamics of the arterial system consisting of an arterial compliance and peripheral resistance called two-element Windkessel model which represented by electric capacitor (C) and resistor (R) respectively as presented in Figure 4.1(a). In the Frank’s Windkessel model, the entire artery was modeled as an elastic chamber with constant arterial compliance [157] where the arterial compliance was the ratio of the total arterial volume change over the arterial pressure change.

(a)

(b)

(c)

Figure 4.1: (a) Two-element Windkessel model, (b) Three-element Windkessel model and (c) Four-element Windkessel model presented in hydraulic and electrical circuits [189].

The developments in computing capabilities and measurement of aortic flow shown that two-element Windkessel model was unable to produce realistic systemic input impedance and aortic pressure waveform when aortic flow was used as input [156, 157]. This result led to the clearly difference between the calculation of input impedance and the measured one in high frequency range as shown in Figure 4.2 [189]. This issue came up with the addition of aortic characteristic impedance to the two-element Windkessel model. Westerhof et al. [188, 191] modified the Frank’s Windkessel model by adding the characteristic impedance (Zc) connected in series with two- element Windkessel known as the three-element Windkessel model as presented in Figure 4.1(b). The characteristic impedance was typically replaced by resistor for the

73 modeling of large artery such as aorta. A relationship between the lumped model and wave travel was represented as characteristic impedance equals to wave speed times blood density divided by cross-sectional area [189]. In 2003, Wang et al. [183] proposed the arterial model in time domain by fit- ting two-element Windkessel model to determine peripheral resistance and arterial compliance. They compared the calculated aortic pressure and flow obtained from Windkessel model with the measured data derived from anesthetized dogs. When the calculated pressure was subtracted from the measured pressure, they found that the difference (excess pressure) was proportional to aortic flow. Thus, the differences in shape between aortic pressure and flow waveform can be predicted realistically by the addition of resistance to two-element Windkessel model. This observation ensured that it was necessary to add the characteristic impedance of aorta as the third element to describe pressure and flow though the entire cardiac cycle, in time domain [189]. In the studies of the three-element Windkessel model, Fogliardi et al. [51] compared the constant compliance and pressure-dependent compliance. Even in the presence of better data fit obtained from pressure-dependent compliance, they concluded that “the nonlinear three-element Windkessel cannot be preferred over the traditional linear version of this model” [51]. The three-element Windkessel model was most widely accepted for systemic circulation modeling because it was able to mimic pressure and flow waveform and fitted well with experimental results [159]. However, the realistic pressure and flow waveform predicted by three-element Windkessel model would be provided when the modeled parameter of capacitor (C) and characteristic impedance (Zc) differed from the actual physiological properties of artery where C and Zc obtained from the standard estimation method tended to be overestimated and underestimated respectively for the time domain fit [159]. Moreover, as shown in Figure 4.2, the error of aortic input impedance predicted by three-element Windkessel model in low frequency range led to the additional of inertance (L) in parallel with the characteristic impedance (Zc) as a fourth element [189]. Burattini and Gnudi [23] suggested this fourth element was an inertance which

74 Figure 4.2: The measured aortic input impedance and impedance predicted by two- element,three-element and four-element Windkessel [189]. equaled to the addition of all inertances (total arterial inertance) in the whole arterial system as presented Figure in 4.1(c). The additional of inertance (L) was able to reduce the errors in the low frequency range and allowed the characteristic impedance

(Zc) to handle with medium and high frequency range [159]. The sample simulation results of three- and four-element Windkessel model were shown in Figure 4.3. Nowadays, the application of Windkessel model was still used in various aspects to explain physiological phenomena. For example, Wesseling et al. [187] computed the aortic ﬂow from the pressure by using nonlinear three-element Winkessel model. Stergiopulos et al. [156, 157, 159] used Windkessel model for estimation of total arterial compliance which played an important role in the determination of systolic and diastolic aortic pressure [158, 160]. Furthermore, Windkessel model was used in the studies of heart assist device [57], heart valve [29, 146] and ventricular afterload [87, 95]. However, Windkessel model was unable to be used in the studies of wave travel and the reﬂections of wave which was the limitation of the lumped model [189].

75 Figure 4.3: Top: schematics of 3- and 4-element Windkessel (WK) models presented in electrical form. Rc and Rp, characteristic and peripheral resistance; C, total arterial compliance; L, inertance. Middle: aortic ﬂow measured in dog. Bottom: measured and model derived aortic pressure [161].

4.2 Review of the Model of Intracranial System

The model of intracranial system can be categorized into two major types of model. First, complex compartment model is the lumped parameter model which is based on the steady state approach to study the behavior of intracranial system represented by electrical elements. Second, pulsatility model is the dynamical model to describe the interaction of intracranial contents during cardiac cycle which focus on the effect of pulsatile nature of blood flow on the variation of intracranial dynamics and properties. Karni et al. [80] considered the Monro-Kellie doctrine as rigid compartment and subdivided into seven compartments as shown in Figure 4.4, then solved for quasi- steady state flow. The resistance flow due to a particular vessel type was lumped at

76 the outﬂow of its compartment. Also, the change in volume of each compartment was represented as an overall compartment property. The compliance was the increasing in volume of one compartments which was equal to the volume displaced from the neighboring compartments.

Figure 4.4: Lumped-parameter seven compartmental model of the cerebrovascular system. [ ] represents pressure in mmHg, ( ) represents ﬂow in ml/min., and <> represents volume in ml [80].

The governing equations for this lumped-parameter compartmental model of cerebrovascular ﬂuid system was the continuity equations for the balance of mass

dP C + ZP = Q (4.1) dt where P was the pressure column vector, Z was the symmetric ﬂuidity (inverse of resistivity) matrix, C was the symmetric compliance matrix and Q was the ﬂux column vector For the steady-state, the equation (4.1) of constant pressure was reduced to

ZP ∗ = Q∗

77 where P ∗ and Q∗ indicated the average, time-independent P and Q respectively. For the non steady-state, Z was determined from the steady state. The equation (4.1) was rearranged into

dP (t) C = Q(t) − ZP (t) dt where C and Z were constant For the quasi steady state, the compliance term was considered to be negligible, dP C dt = 0. Then, equation (4.1) became

ZP (t)= Q(t)

However, this model did not relate events to their spatial localization which was the limitation of a compartmental approach. Czosnyka et al. [35] studied the time-dependent interactions between pressure, flow, and volume of cerebral blood and CSF through the hydrodynamic equivalent of the model which contained two major flow pathways as presented in Figure 4.5. As shown in Figure 4.6, the equivalent electrical circuit corresponded directly to the hydrodynamic structure (Figure 4.5) and was described by set of non-linear differential equations:

dP 1 ABP − P P − P P − P i = ( a − i ss − v ss ) dt Ci Ra RCSF Rb dP dP 1 P − P P − P v = i + ( a v − v ss ) dt dt Cv CV R Rb

dPa dPi 1 ABP − Pa Pa − Pv = + ( − − If ) dt dt Ca Ra CV R

This model simulated changes in arterial blood inflow and storage, arterial and capillary blood flow controlled by cerebral autoregulation, venous blood storage and venous outflow modulated by changes in ICP and CSF storage and reabsorption. Both autoregulating and non-autoregulating system were simulated and compared.

78 Figure 4.5: Hydrodynamic equivalent of the model, comprising pathways of CBF and the CSF circulation.A rigid skull is represented by the outer box, with a compensatory reserve Ci associated with the compliant dural sac within the lumbar channel [35].

Figure 4.6: Electrical circuit equivalent to the hydrodynamic model [35].

Ursino and Lodi [171] constructed lumped-compartmental model to describe the hemodynamics of the arterial-arteriole cerebrovascular bed, CSF production and reabsorption processes, the nonlinear pressure-volume relationship of the craniospinal compartment, and a Starling resistor mechanism for cerebral veins as shown in Fig- ure 4.7. The interaction between ICP,cerebral blood volume and autoregulation were simulated where resistance and compliance were actively adjusted by the action of cerebrovascular control mechanism. Also, three diﬀerent related phenomena were analyzed: the generation of plateau waves, the eﬀect of acute arterial hypertension

79 on ICP, and the role of cerebral hemodynamics during pressure-volume index (PVI) tests. This model was able to reproduce various clinical results, such as the pattern of ICP pulsatile change, the origin of pathological self-sustained ICP wave and the different ICP responses to fluid injection into or fluid removal from the craniospinal space. The authors suggested that PVI testing used to extract information not only 1 on intracranial compliance (Cic = , where kE was elastance coefficient of the kE Pic craniospinal system) and CSF circulation, but also on the status of mechanisms con- trolling cerebral blood flow. ICP pulsatility was affected by large intracranial arteries and venous circulation. However, this model was unable to be used to study ICP pulsating wave synchronous with cardiac beat.

Figure 4.7: Electric analog (A) and corresponding mechanical analog (B) of intracranial dynamics according to present model. Cerebral blood flow (CBF,q) enters skull at pressure approximately equal to systemic arterial pressure (Pa). Arterial-arteriolar cerebrovascular bed consists of a regulated capacity (Ca), which stores a certain amount of blood volume, and a regulated resistance (Ra), which accounts for pressure drop to capillary pressure (Pc). At capillary level, cerebrospinal fluid (CSF) is produced through a CSF formation resistance (Rf ). CBF then passes through venous cerebrovascular bed, mimicked as series arrangement of proximal venous resistance (Rpv) and resistance of collapsing lateral lacunae and bridge veins (Rdv). Model assumes that, because of collapse of last section, cerebral venous pressure (Pv) is always approximately equal to intracranial pressure (Pic). Finally, CSF is reabsorbed at venous sinus pressure (Pvs) through CSF outflow resistance (Ro). Intracranial pressure is determined by amount of volume stored in nonlinear intracranial compliance (Cic). This volume results from a balance between CSF inflow (qf ), CSF outflow (qo), blood volume changes in arterial capacity, and mock CSF injection rate (Ii). Modified from Ursino and Lodi [171].

80 Lakin et al. [89] introduced 16-compartment whole-body model for intracranial pressure as illustrated in Figure 4.8. This model developed the Monro-Kellie doctrine by adding a spinal-subarachnoid CSF compartment bridged intracranial and extracranial physiology allowing the buffering effects of intracranial pressure fluctu- ations by the spinal theca. The physical constituents in subunits were blood, CSF, and tissue and interstitial fluid. The body first was divided into intracranial and extracranial compartments. The extracranial compartment was subdivided into a lower region (below the pelvis) and a central region (between the pelvis and clavicles). The vascular system in each compartment was divided into artery, capillary, and vein. In order to maintain the production of CSF by autoregulation, the choroid plexus was placed in a separate compartment. Each compartment in the model was defined by a lumped, i.e. time-dependent function. Volume interactions took place at the interfaces between compartment through input and output bulk flow or through bulk membrane deformations across adjacent compartment. This model also included the interaction between the external environment through flows representing the inges- tion and elimination of fluid via the central body, as well as the transfer of fluid between capillaries and tissue by filtration defined by the Starling-Landis equation, and lymphatic system. However, previous complex compartment model did not cooperate the pulsatile nature of arterial flow. This arterial pulsatile flow related to interaction of intracranial contents that significantly described Windkessel mechanism within rigid cranium. In 2001, Egnor et al. [46] applied mathematical model to describe oscillation of blood and CSF, represented by phasors on the complex plane, and analyze of pulsatile motion within the cranium which was the first CSF pulsatile dynamics model as shown in Figure 4.9(a). The authors performed the simulation of intracranial pulsations in case of normal intracranial dynamic (resonance) and diminished intracranial compliance (elevated ICP) where their mathematics governing the oscillations of the CSF space was

81 Figure 4.8: The 16 compartment whole-body model. A ﬁlled arrow indicates a one- way ﬂow and a hollow arrow indicates a pressure dependent resistance. Compartment labels are enclosed in parentheses with the spatially-averaged mean pressures in square brackets. The thick line indicates the cranial wall [89].

F0 sin ωt = mCSF x¨CSF (t)+ Rx˙ CSF (t)+ kExCSF (t)

The oscillations was able to be simulated through a series RLC electrical circuit as presented in Figure 4.9(b), based on the analogy between mechanical and electrical oscillation summarized in the Table 4.1. Also, the pulsatile cerebral blood ﬂow and the Windkessel eﬀect had been simulated through two degree of freedom mass spring system as presented in Figure 4.10(a) and equivalent RLC circuit as presented in Figure 4.10(b). This motion of blood and

82 (a) (b)

Figure 4.9: (a) A model of CSF pulsation with a single degree of freedom.The CSF pulsation, which is the mass of CSF (mCSF ) displaced by the maximum expansion of the vessel is represented by sphere. The instantaneous displacement of the CSF pulsation is represented by xCSF (t). The external force of the vascular pulsation is assumed to be sinusoidal, and given by F0 sin ωt. The other forces acting on the pulsating CSF include a resistance force Rx˙ CSF (t) and an elastic force kExCSF (t), representing the elasticity of the walls of the space. The net force acting on the CSF pulsation is the inertial force mCSF x¨CSF (t). (b) Equivalent RLC electrical circuit for CSF pulsation. Modiﬁed from Egnor et al. [46].

Table 4.1: Summary of the equivalent between pulsation of CSF and oscillations of electricity in an AC electrical circuit [46]

CSF were governed by

mbloodx¨blood(t)+(kblood + kCSF )xCSF (t)+ kCSF xCSF (t) = Fheart sin ωt

mbloodx¨blood(t)+ kCSF (xCSF (t) − xblood(t)) = 0

This model was able to be concluded that Windkessel mechanism would be eﬀec- tive if CSF space was oscillating in or near resonance which depended on the speciﬁc value of inertia, elasticity and heart rate. However, Tenti et al. [166] countered Egnor et al.’s conclusion that “the synchrony of arterial and CSF pulsations is not due to

83 (a) (b)

Figure 4.10: (a) The intracranial Windkessel effect, which is the dissipation of arterial pulsations into the CSF, can be modeled by representing the intracranial blood and CSF as two separate masses connected by springs representing the elastic elements of vasculature and craniospinal contents. (b) The electical analog to a mechanical absorber is a wave trap, which is main RLC circuit representing the capillary blood and a smaller parallel RLC circuit representing the CSF. Modified from Egnor et al. [46]. resonance” [166]. In 2002, Egnor et al. [47] extended their previous model of pulsation by focusing on communicating hydrocephalus. This model was still based on the equivalent pulsatile motion of blood and CSF in an electrical circuit as shown in Figure 4.11. The model simulated dynamic of normal intracranial pulsatile and the salient features of communicating hydrocephalus such as ventricular dilation, intracranial pressure waves, narrowing of the CSF-vanous pressure gradient, diminished cerebral blood flow, elevated resistive index and malabsorption of CSF. From this pulsation model’s result, “malabsorption of CSF is the result, not the cause, of communicating hydrocephalus” [47] which differed from traditional theories. The author also concluded that “communicating hydrocephalus is a disorder of intracranial pulsations” [47]. However, due to a simple sinusoidal waveform was used as initial forcing function instead of cardiac output function in Egnor et al.’s model [46, 47], the realistic response in term of waveform and timing was distorted. Linninger et al. [101] proposed the fluid-structure interaction model to predict pulsatile flow and pressures of CSF through the brain’s ventricles based on the first principles of fluid mechanics with linear elasticity. The goal of this model was to

84 Figure 4.11: The intracranial filter circuit and the windkessel mechanism. Intracranial blood vessels and CSF spaces are arranged as parallel pathways branching from a series flow. Normal intracranial blood flow and CSF dynamics can be represented by a series-parallel array of blood vessels and CSF spaces. Modified from Egnor et al. [47]. simulate ICP and CSF velocity during normal and hydrocephalus condition for comparison with clinical and MRI data. The first principles model for pulsatile CSF flow related three dynamically interacting system: the cerebral vascular system, the CSF-filled ventricular and subarachnoid space, and the brain parenchyma. As presented in Figure 4.12(a), arterial blood flowed into the expandable choroid plexus caused it to expand and acted like a pump to drive the pulsatile CSF circulation. CSF transmitted the lateral ventricles (V1 and V2) to the third ventricle (V3) via the foramen of Monro (FM), the fourth ventricle (V4) via the aqueduct of Sylvius (AS), reached the subarachnoid space (SAS) via foramen of Luschke (FL), and then CSF was reabsorbed into the sagittal sinus. However, no absorption of CSF by parenchyma was assumed. The governing equation of discretized model of CSF flow (Figure 4.12(b)) was

85 (a) (b)

Figure 4.12: (a) Schematic of CSF pathways, the vascular system and brain parenchyma. (b) The discretized model of CSF ﬂow induced by choroid expansion a(t). Modiﬁed from Linninger et al. [101]. cyclic motion of choroid plexus followed the cardiac cycle by forcing function

π 1 π a(t)= α(1.3 + sin(ωt − ) − cos(2ωt − )) 2 2 2

The equation for the acceleration of the elastic tissue

(ρwAiδ)¨yi(t)+ kdy˙i(t)+ keyi(t) − Ai[Pi(t) − P0(t)]=0, i ∈{V 1 − V 4,SAS} where k was linear spring elasticity The continuity of CSF ﬂow in the ventricles

∂{A [h + a(t)+ y (t)]} i i i = q − q , i ∈{V 1 − V 4} ∂t f,i i

The elastic foramina was governed by the axial momentum equation

∂vi ∂vi ∂Pi(t) 8µ ρ[ + vi ]+ = −Fi = − 2 vi, i ∈{FM,AS,FL} ∂t ∂z ∂z ri

For subarachnoid space (SAS), the continuity equation was

∂{Ai[hi + yi(t)]} = qj− − qe,j , j ∈{SAS} ∂t 1

86 and diffusive reabsorbtion of CSF qe,j = κ[pj (t) − p0(t)] where κ was reabsoption constant. Also, 2-D computational fluid dynamic (CFD) simulations and a set of simple hydraulic experiment to explain the expansion of lateral ventricles were included in this paper. The model clarified the role of ICP rise during the formation of communication hydrocephalus. “The rise is not a cause of hydrocephalus, but an effect of increased fluid due to lowered absorption of CSF” [101]. This model had been modified in Masoumi et al.’s model [115] by considering CSF pulsatile formation as the principal driver of CSF motion instead of the choroid plexus expansion. In 2009, Linninger et al. [102] constructed the multi-compartment mathematical model to simulate the intracranial dynamics for normal and pathological conditions, i.e. communicating hydrocephalus. MRI-data and the predicted results were compared. As presented in Figure 4.13, this model was designed for predicting the force interaction of three main elements; 1) blood flow through cerebral vasculature which was divided into arteries (Ar), arterioles (Al), capillaries (Cp), veinules (Vl), veins (V ) and venous sinus (vSinus), 2) the CSF system was included the lateral (Lv), third (3V ) and fourth (4V ) ventricles, cerebral subarachnoid space (SAS) and the spinal canal, 3) the left and right brain parenchyma were treated as a bi-phatic medium composed of extracellular fluid and a solid cell matrix. Flow through each compartment of cerebral vasculature and CSF system were governed by three principle equations: The continuity equation

∂A l = f − f ∂t in out where l was the length of compartment, A was a cross-sectional area, fin and fout were the volumetric ﬂow rate in and out of compartment, respectively. The axial momentum equation governed by Hagen-Poiseuille law

Pin − P =∆P = afin

87 Figure 4.13: The Linninger et al.’s multi-compartment model with one arterial pressure in the carotid Pinit as input signal and the venous pressure in the jugular vein is Pout. Modiﬁed from Linninger et al. [102].

2 where a was ﬂow resistance (a = 8πµl/A ), µ was ﬂuid viscosity and Pin and P were the upstream and current compartment pressure, respectively. Compartment expansion or compression

A − A0 Plumen − Pbrain = E( ) A0 where Plumen-Pbrain was the pressure diﬀerence between the vessel lumen and the bi- phasic brain compartment, E was vessel’s elastance and A − A0 was the change in a vessels cross-sectional area. This model also strictly satisﬁed the Monro-Kellie doctrine for each brain hemisphere where total volume of all parenchyma, blood and CSF compartment remained constant. The predicted results from this model were in well agreement with various aspect of clinical data such as pulsatility index and pressure-volume index (PVI).

88 However, the inertia term had been neglected for convenience and avoiding wave re- ﬂection problem. The authors suggested that the inertia term should be included, especially for large arteries.

89 Chapter 5

Mathematical Model

The goal of this mathematical model is to study hemodynamics of major arteries and intracranial system based on Windkessel mechanism by simulating the human cardiovascular system which is the blood flow from heart through the network of elastic blood vessel. In this mathematical model, ascending aorta is considered as the first blood vessel that pulsatile blood flow through. Then assume that 30% of blood supply to upper limbs and 70% to lower limbs. For hemodynamics of lower limbs, blood after passing ascending aorta then flow through three set of arteries to femoral artery including descending aorta, common iliac artery, external iliac artery successively before reaching femoral artery. For upper limbs and cerebral blood flow, blood after passing ascending aorta then flow to left and right side of upper body including left and right hands via subclavian artery, and left and right hemispheres via common carotid artery and internal carotid artery. Intermittently pumping action of heart generates pulsatile blood flow throughout the body in the time interval called cardiac output. As shown in Figure 5.1, cardiac output (Qin) is simulated by the combination of three sets of sinusoidal wave which acted as the input of the model:

11 11 5 Qin = 350(sin(ωt)) + 150(sin(ωt + 0.11)) + 20(sin(ωt + 0.45)) where ω is the heart rate which is randomly created between range of ω = 2.3π −2.4π

90 radian/second.

Initial Cardiac Output

350

300

250

200

150

100

50 Cardiac Output (ml/sec.)

0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (sec.)

Figure 5.1: The initial pulse cardiac output, generated by heart, is the combination of three sets of sinusoidal wave with random heart rate.

To compare the dynamic response for diﬀerent intracranial conditions, three cases of simulation are considered: (1) normal condition, (2) the case of neurosurgical disorder and (3) the case of treatment by using a medical balloon. The basis for Windkessel mechanism of major arteries and intracranial system will be described by the following equations:

5.1 Continuity Equation

During systole, cardiac contraction discharges entire stroke volume of blood into the arterial system. About 50% of blood flow forward to the peripheral circulation while the remainder is stored within the arterial system [16] which provided by elastic expansion of arterial wall (section 5.2) and peripheral resistance (section 5.3 and 5.4). During diastole, this elastic artery passively recoils and forces the storage volume into peripheral circulation [16]. To analyze the flowing fluid within vessel, the basic concept of Windkessel mechanism is described by the principle of conservation of mass called the continuity equation. The rate of volumetric flow into blood vessel

91 Qin is equal to the rate of stored ﬂow Qstored plus the rate of ﬂow out of blood vessel

Qout, which is given by

Qin = Qstored + Qout dV dx Q − Q = Q = vessel = A vessel in out stored dt vessel dt 2 Qin − Qout = π(x0,vessel +∆xvessel) ∆˙xvessel (5.1) where x0,vessel is initial radius of blood vessel and ∆xvessel is radius displacement of blood vessel.

5.2 The Equation for the Acceleration of the Elas- tic Blood Vessel

∆xvessel kvessel − kvessel∆xvessel

x0,vessel Pblood mblood mblood

PbloodAvessel

lvessel (a) (b)(c)

Figure 5.2: (a) Cross-sectional area of blood vessel (b) Elastic blood vessel (c) Free body diagram of blood with pressure and elastic forces exerting on

To describe the buﬀering function of Windkessel mechanism which accommodates the extra blood during systole and drive blood out during diastole, the pulsatile blood ﬂow through the expansion and contraction of elastic vascular wall are represented by two type of forces act on the pulsatile blood. As illustrated in Figure 5.2, pressure 2 force exertedby the blood (Fblood = PbloodAvessel = Pbloodπ(x0,vessel+∆xvessel) ) and the elastic force representing elasticity of the blood vessel based on Hooke’s law (Fspring =

92 kvessel∆xvessel) are equal to total force exerted on blood which is the force of inertia mbloodablood = ρbloodVvessel∆¨xvessel. The motion of arterial pulsation is represented by the equation

Fblood + Fspring = mbloodablood

PbloodAvessel − kvessel∆xvessel = ρbloodVvesselablood

2 Pbloodπ(x0,vessel +∆xvessel) − kvessel∆xvessel = ρbloodVvessel∆¨xvessel (5.2)

2 where Vvessel = π(x0,vessel +∆xvessel) lvessel, Pblood is blood pressure, kvessel is blood vessel’s stiffness, ρblood is the density of blood and lvessel is blood vessel’s length Another significant parameter describing Windkessel mechanism for filtering pulsatile inflow into non-pulsatile outflow is the peripheral resistance which can be represented by two different equations:

5.3 Hagen-Poiseuille’s Law

∆xvessel

x0,vessel Qin Qout

Pin Pout

lvessel

Figure 5.3: Hagen-Poiseuille’s law represent the blood flow resistance caused by the length of artery in term of the pressure drop between inflow and outflow.

Hagen-Poiseuille’s law describe the pressure drop between inflow and outflow in a long narrow tube with assumption of laminar and incompressible flow as shown in

93 Figure 5.3. This ﬂuid dynamics’s law represents the blood ﬂow resistance due to the length of artery which is given by

4 (Pblood − Pout)πrvessel Qout = 8µbloodlvessel

8µbloodlvesselQout Pblood = Pout + 4 (5.3) π(x0,vessel +∆xvessel)

combining equation (5.1) and (5.3)

2 8µbloodlvessel(Qin − π(x0,vessel +∆xvessel) ∆˙xvessel) Pblood = Pout + 4 (5.4) π(x0,vessel +∆xvessel)

where µblood is dynamic viscosity of blood, Qout is volumetric ﬂow rate of blood outﬂow, and Pout is pressure in blood vessel’s outlet. The continuity equation (equation 5.1) combine with the equation for the acceleration of elastic blood vessel (equation 5.2) and Hagen-Poiseuille’s law (equation 5.3) are applied for all extracranial arteries and intracranial capillaries and veins.

5.4 The Relationship of Flow and Pressure in Ori- ﬁce

∆xvessel

Qin x0,vessel xout Qout

Pblood Pout

Figure 5.4: The relationship of flow and pressure in orifice represented the peripheral resistance of blood flow due to the change of lumen size.

94 As shown in Figure 5.4, the mechanical device called “orifice” represented the peripheral resistance of blood flow. Orifice is used for measuring the fluid flow rate through the differences in pressure from the upstream side to the downstream of a partially obstructed pipe which based on the Bernoulli’s principle to describe the relationship between the pressure and velocity of fluid. This equation describes blood flow from large artery to smaller with resistance due to the change of vascular lumen diameter which is represented by

Qout = α Pblood − Pout (5.5) p 2 2 Aout 2 πxout where α = A = , ρblood 1−( out )2 ρblood 2 q Avessel v 2 q q u − πxout u1 2 u π(x0,vessel+∆xvessel) t where xout is radius of blood vessel’s outlet combining equation (5.1) and (5.5)

(Q − π(x +∆x )2∆˙x )2 P = P + in 0,vessel vessel vessel (5.6) blood out α2

The continuity equation (equation 5.1), the equation for the acceleration of elastic blood vessel (equation 5.2), and the relationship of ﬂow and pressure in oriﬁce (equation 5.5) are applied for intracranial arteries.

5.5 Blood Flow through Cranium

For intracranial system, the cerebral blood flow from artery to capillaries and vein through intracranial cavity is presented in Figure 5.5. For the brain protection, intracranial system has a unique characteristic which is different from any other part of the body, i.e. enclosed within a fixed volume of rigid cranium based on Monro- Kellie doctrine. Moreover, the pressure inside the cranium called intracranial pressure

(PICP ) which exerts against the displacement of arterial and venous wall is additional force in intracranial system (Figure 5.5(a)). Hence, equation (5.2) has been modiﬁed into

95 2 (Part − PICP )π(x0,art +∆xart) − keq,art∆xart = ρbloodVart∆¨xart (5.7)

kartkCSF where keq,art = for arterial blood kart+kCSF

2 (Pcap)π(x0,cap +∆xcap) − kcap∆xcap = ρbloodVcap∆¨xcap (5.8)

for capillary blood

2 (Pvein − PICP )π(x0,vein +∆xvein) − keq,vein∆xvein = ρbloodVvein∆¨xvein (5.9)

kveinkCSF where keq,vein = for venous blood kvein+kCSF

where Part,Pcap,Pvein and PICP are arterial, capillaries, venous blood pressure and intracranial pressure, respectively.

PICP

−PICP Aart − keq∆xart − kcap∆xcap ∆xart

∆xvein x0,art Qin xout x0,vein mblood mblood Part Pvein

P A art art PcapAcap

(a) (b) (c)

Figure 5.5: (a) There are three forces exerting arterial and venous blood. (b) Blood ﬂow through artery, capillaries and vein in the enclosed cranium space. (c) There are only two forces exerting on capillary blood.

To maintain continuous cerebral blood ﬂow and to ensure pulseless ﬂow through cerebral capillaries, the additional pulsation absorber is required which provided by

96 kCSF

keq

kart

Figure 5.6: Combination of blood vessel’s stiffness (kart and kvein) and stiffness of elastic intracranial contents (kCSF ) in series result in less equivalent stiffness (keq) or more intracranial compliance of the CSF system the elastic properties of other intra- and extracranial contents (i.e. brain tissue, intracranial subarachnoid space, and spinal thecal sac). As shown in Figure 5.6 the combination of blood vessel’s stiffness (kart and kvein) and stiffness of elastic intracranial contents (kCSF ) in series result in less equivalent stiffness (keq) which provide more intracranial compliance to the CSF system.

5.6 Pressure-Volume Relationship

Monro-Kellie doctrine states that the total volume (Vtotal) of cranium is constant.

Any increase in the volume of intracranial content (e.g. arterial blood Vart, venous blood Vvein, brain or CSF) will bring about the decrease in the volume of another. However, only interaction of three intracranial contents (arterial blood, venous blood and CSF) are considered in this model because brain expansion is typically very small in the healthy individuals (about 2% of the arterial expansion [66]). During the systolic expansion of cerebral arteries, ICP (PICP ) rises with the expulsion of extraventricular CSF downward through foramen magnum to contractible spinal theca located in lumber space. This mechanism allows the pulsatile energy from intracranial space to absorb in spinal region because spinal subarachnoid space has higher compliance during systole (and vice versa during diastole) [133]. During diastole, elastic arteries passively recoil with ICP falls and CSF ﬂow back into intracranial space. In

97 this model, this pressure-volume compensatory mechanism between intracranial and spinal region is imitated by the displacement behavior of piston in cylinder ﬁlled with compressible ﬂuid. Thus, the absolute ICP and residual volume (Vtotal − Vart − Vvein) in intracranial space are inversely proportioned along exponential curve which represented by

P V = constant

PICP (Vtotal − Vart − Vvein) = constantICP (5.10)

5.7 Interhemispheric Pressure Gradients

Left Hemisphere Right Hemisphere vein vein

PICP,L PICP,R artery artery

(a)

−PICP,LAmid −PICP,RAmid − kmid∆xmid

(b)

Figure 5.7: (a) Intracranial space is divided into left and right hemispheres with midline displacement to describe the transmission of pressure and volume between left and right cerebral hemispheres. (b) Free body diagram of midline displacement.

98 Generally, cranium is considered as a single rigid compartment with uniform distribution of ICP over entire intracranial space [39]. However, diﬀerences in ICP between two hemispheres (interhemispheric ICP gradients) were observed in many experimental studies in animal and clinical case reports in patients with head injury. In this mathematical model, the intracranial space is divided into left and right hemispheres as presented in Figure 5.7. A movable separator is constructed to represent the center line or midline in order to describe the transmission of pressure and volume between left and right cerebral hemispheres. The equation for midline displacement is given by

(PICP,L − PICP,R)Amid − kmid∆xmid = mmid∆¨xmid (5.11)

Thus, the pressure-volume relationship within the rigid cranium and between left and right cerebral hemisphere become

PICP,L((VL + Amid∆xmid) − Vart,L − Vvein,L) = PICP,R((VR − Amid∆xmid) − Vart,R − Vvein,R) = constant (5.12)

where PICP,L and PICP,R are left and right hemisphere intracranial pressure, Amid is the cross-sectional area of midline, kmid is midline tissue’s stiﬀness, mmid is the mass of midline, ∆xmid is the displacement of midline, VL and VR are left and right hemispheric volume, Vart,L and Vart,R are left and right arterial blood volume, and

Vvein,L and Vvein,R are left and right venous blood volume.

5.8 Interhemispheric Asymmetry of Cerebral Blood Flow

A steady cerebral blood supply is required to provide a normal function of central nervous system. However, most of severe intracranial disorders are associated with decreased global and regional cerebral blood flow. One major cause of cerebral blood flow reduction is the compression of cerebrovascular bed. The smaller vascular diameter markedly increase the resistance of blood flow which reduce cerebral blood flow

99 below the level needed to meet the metabolic demands of the brain [193]. Hence, the idea of flow through parallel pipes with different diameters (Figure 5.8) is applied to describe blood flow to hand and cranium. Also, the interhemispheric asymmetry of cerebral blood flow is studied with two following conditions: (1) The principle of continuity, total blood flow to each side of upper body equal to summation of blood flow to each side of hand (QL,hand and QR,hand) and cranium

(QL,cranium and QR,cranium). Also, total blood ﬂow of left side (QL,total) and right side

(QR,total) are equal.

QL,hand + QL,cranium = QL,total = QR,total = QR,hand + QR,cranium

(2) Blood ﬂow depend on the cross-sectional area of artery

Q A V Q A V L,hand = L,hand L,hand , R,hand = R,hand R,hand (5.13) QL,cranium AL,craniumVL,cranium QR,cranium AR,craniumVR,cranium and assume that blood ﬂow velocity (V ) to hand and cranium are approximately equal, then equation (5.13) can be modiﬁed to

Q A Q A L,hand = L,hand , R,hand = R,hand (5.14) QL,cranium AL,cranium QR,cranium AR,cranium

5.9 The Case of Neurosurgical Disorder

Space-occupying lesion is typically observed in patients with TBI. TBI can cause the internal bleeding (hemorrhage) from an injured blood vessel. This abnormal accumulation of bleeding blood brings a mass effect called mass lesion. Most common type of intracranial mass lesion is hematoma. A formation of hematoma will occupy the space within the skull which essentially has a finite volume. In this mathematical model, the interhemispheric asymmetry of ICP and cerebral blood flow will be observed. Unilateral mass lesion is created by placing the volume of mass lesion

100 QL,cranium QR,cranium

QL,hand QR,hand

QL,total QR,total

Ascending Aorta

Figure 5.8: Blood ﬂow to hand and cranium after passing ascending aorta

(Vlesion) in the right cerebral hemisphere. Also, the intracranial dynamic response to space-occupying mass lesion will be observed. Then equation (5.12) become

PICP,L((VL + Amid∆xmid) − Vart,L − Vvein,L) =

PICP,R((VR − Amid∆xmid) − Vart,R − Vvein,R − Vlesion) = constant (5.15)

5.10 The Case of Treatment by using a Medical Balloon

Practically, the only way to restore cerebral blood flow is to remove the tumor or accumulated fluid by shunting [193]. Shunting is commonly used to relieve the patients who suffer from hydrocephalus or disorders related to reduced cerebral blood flow. However, there are many complications associated with shunting procedures including shunt dependency, infection, over-drainage of CSF and development of the slit ventricle syndrome (SVS) [180]. Moreover, no significant improvement of CBF after shunting was observed in some case reports [72, 88, 109, 116, 127]. Thus, a med-

101 ical balloon is introduced as an alternative treatment device. The medical balloon is a medical device with a wide range of clinical applications such as cardiological, neurological and vascular application. In animal-testing laboratory research at Cleve- land clinic, the medical balloon is inserted into animal’s right cerebral hemisphere. Then, the balloon is pressurized intermittently, by air compressor, along the cycle of intracranial pressure (ICP). As shown in Figure 5.9, there are three different balloon cycle (1) augmentation, (2) reduction and (3) inversion used to increase cerebral blood flow. Likewise, in this mathematical model, medical balloon is placed in the right cerebral hemisphere and applied three different balloon cycle for treatment purpose which is to maximize cerebral blood flow. CARDIAC CYCLE (msec)

0 100 200 300 400 500

Peak ICP 200 Amplitude

(mmHg) 150

AUGMENTATION 0

PRESSURE REDUCTION -150 INVERSION

-200

Figure 5.9: Three different balloon cycle including augmentation, reduction and inversion used to increase cerebral blood flow. Modified from laboratory research data at Cleveland clinic

102 Chapter 6

Simulation Results

The methematical model is implemented in Simulink to study the hemodynamics throughout human major arteries and intracranial system which based on Windkessel mechanism. For intracranial system, the simulations focus on intracranial pressure (ICP) and the interaction of main intracranial contents based on Monro-Kellie doctrine. To compare the dynamic response for diﬀerent intracranial conditions, the simulation results can be categorized into three cases: (1) normal condition, (2) the case of neurosurgical disorder and (3) the case of treatment by using a medical balloon.

6.1 Normal Condition

In case of normal condition, the simulations focus on the blood flow throughout major arterial system of human based on Windkessel mechanism which include blood supply to lower and upper limbs. The heart intermittently pumps blood out along the cardiac cycle as pulsatile nature of blood flow called cardiac output. The first set of elastic artery that blood passing through is ascending aorta to aortic arch. After that, some of blood flow upward to supply upper limbs and intracranial system which is assume to be about 30% of total blood volume. The remainders (about 70%) flow downward to supply abdominal cavity and lower limbs. In term of timing and waveform, the

103 relationship of blood ﬂow or pressure signal between lower body especially at femoral artery and intracranial system can be compared in this simulation.

6.1.1 Lower Body

Cardiac output, first generated by heart, is used as initial input of the system. Pul- satile blood flow through major arteries to lower limbs with different diameter and elastic property. In this model, four sets of major artery are considered including (1) ascending aorta to aortic arch, (2) aortic arch to common iliac artery via the longest part of the aorta called descending aorta, (3) common iliac artery to external iliac artery, and (4) external iliac artery to femoral artery. As shown in Figure 6.1, the phase lag and less pulsatility of predicted blood outflow waveform after passing each set of major artery. The predicted result is caused by the effectiveness of Windkessel mechanism which provided by the expansion of artery and flow resistance due to the length of artery. This also show that buffering function of large arteries acts as hydraulic filter of the cardiovascular system which converts pulsatile flow generated by heart to the continuous steady state flow through capillary bed for exchanging process. As illustrated in Figure 6.2, pressure and velocity pulse waveforms in the aorta and arterial branches of a dog from Caro et al. [26] have characteristic pulsatile waveforms in different parts of arterial system. Also, the delay of pulse pressure waveform after arterial blood flow waveform presented in arterial system are agree with the predicted results, for example, at ascending aorta and at common iliac artery as shown in Figure 6.3 and Figure 6.4 respectively.

6.1.2 Upper Body and Intracranial Space

Most of the blood supply into intracranial space via left and right internal carotid arteries which branches from each side of common carotid arteries. For normal condition, cerebral blood ﬂow to left and right hemispheres are bilaterally equal and without

104 Arterial Blood Flow to Lower Body

350 Cardiac Output Qout@Aortic Arch Qout@Common illiac Artery Qout@External illiac Artery 300 Qout@Femoral Artery

250

200

150

100

50 Blood Flow (ml/sec.)

3.4 3.5 3.6 3.7 3.8 Time3.9 (sec.)4 4.1 4.2 4.3 4.4

Figure 6.1: Arterial blood flow through major arteries to lower limbs. Cardiac output (dark-blue), generated by heart, flow into ascending aorta and flow out at aortic arch (green). Then, blood flow into descending aorta to common iliac artery (orange), pass through external iliac artery (blue) and femoral artery (purple). interhemispheric ICP gradients. Hence, no midline displacement is found. As shown in Figure 6.5, the effectiveness of intracranial Windkessel mechanism converts the pulsatile arterial inflow to less pulsatile arterial outflow with significant phase shift. The intracranial Windkessel mechanism is provided by overall intracranial compliance (combination of vascular compliance and elastic property of intra- and extracranial contents) and peripheral resistance due to partial obstruction from change of vascular lumen diameter. However, intracranial capillary and venous outflow perform almost identical waveform to arterial outflow. In Figure 6.6, blood pressure in intracranial artery is highest with widest arterial pulse pressure and becomes lower in capillary and vein respectively. The different width of pulse pressure in each pulsatile cycle is caused by the different heart rate which randomly created by cardiac action. This result also leads to random variation of intracranial contents’ dynamic and ICP waveform during cardiac cycle. The phase relationship of predicted blood flow and pressure waveform in the intracranial space are in agreement with Avezaat et al.’s MRI data from dog [6] which presented in Figure 6.7). As illustrated in Figure 6.8, the peak of intracranial pres-

105 Figure 6.2: Pressure and velocity pulse waveforms in the aorta and arterial branches of a dog. Note that the pressure maximum becomes ampliﬁed while the velocity maximum decreases as the blood moves downstream [26] .

106 Ascending Aortic Blood Pressure and Flow 130

125

120

115

110

105

100

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3

350 Pressure(mmHg)

300

250

200

150

100

50 Flow(ml/s)

0 3.3 3.4 3.5 3.6 3.7 Time3.8 (sec.)3.9 4 4.1 4.2 4.3

Figure 6.3: Ascending aortic blood pressure and ﬂow waveforms.

Common Iliac Arterial Blood Pressure and Flow 70

Flow(ml/s) 0

3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 105

100

70 Pressure 65

60 3.4 3.5 3.6 3.7 Time3.8 (sec.)3.9 4 4.1 4.2 4.3

Figure 6.4: Common iliac arterial blood pressure and ﬂow waveforms.

107 Intracranial Blood Flow 35 Qin@Common Carotid Qout@Common Carotid Qout@Capillaries 30 Qout@Vein

5 Blood Flow(ml/sec.)

0 2.6 2.7 2.8 2.9 3Time3.1 (sec.)3.2 3.3 3.4 3.5 3.6

Figure 6.5: Blood, after passing ascending aorta, flows into intracranial artery (dark blue) and capillaries (green) then flows into intracranial vein (red). Blood exits the intracranial space via intracranial vein represented by blue waveform. sure (ICP), cerebral blood volume (CBV), arterial blood pressure (ABP), and arterial blood outflow are synchronized which delay after arterial blood inflow to cranium. In Figure 6.9, the intracranial dynamics related to the demand of intracranial contents according to Monro-Kellie doctrine are simulated. The systolic expansion of intracranial arteries leads to synchronously compression of intracranial vein and reduction of intracranial volume. Also, the delay of arterial outflow after expansion of arterial inflow due to Windkessel mechanism leads to delay of capillary dilation (brain parenchymal expansion). The phase relationship of predicted pulsatile blood flow has a good correlation with the diagram of phase relationship of blood and CSF velocity waveform observed by Greitz [61] by using flow-sensitive MRI technique as presented in Figure 3.4. Femoral artery is commonly selected as site of transducer insertion for arterial blood pressure (ABP) monitoring. As shown in Figure 6.10 (upper), the timing relationship between ABP at femoral artery and ICP signal in canine’s experimentation conducted by Cleveland clinic researchers are observed. The small delay of ABP at femoral artery and ICP signal found in this animal observation is in agreement with the predicted result from this mathematical model based on human physiology as shown in Figure 6.10 (lower). This correlation may result from the different distance

108 Intracranial Blood Pressure 90

40 P@Common Carotid P@Capillaries P@Vein 30

10 Blood Pressure (mmHg)

0 1 2 3 4 5 6 7 Time (sec.)

Figure 6.6: Arterial (dark blue), capillary (green), and venous (red) blood pressure in the intracranial space.

Figure 6.7: Plot of vertebral artery pulsatile change in cerebral blood volume (CBV) and ventricular ﬂuid pressure (VFP) during ﬁve cardiac cycles in dog. Note also the synchronization of the extreme values of the change in CBV and CSF pulse [6].

109 14

11 ICP

10 3 3.5 4 4.5 5 5.5 6 95

80 CBV 75 3 3.5 4 4.5 5 5.5 6 100

60 ABP 40 3 3.5 4 4.5 5 5.5 6 40

10 Flow 0 3 3.5 4 4.5 5 5.5 6 Time (sec.)

Figure 6.8: The phase relationship of predicted blood flow and pressure waveform in the intracranial space show that intracranial pressure (ICP), cerebral blood volume (CBV), intracranial arterial blood pressure (ABP) and arterial blood outflow (dark blue) are in-phase which delay from arterial blood inflow (black). ICP and ABP are in mmHg. CBV is in ml. Arterial blood inflow and outflow are in ml/sec. This figure is in agreement with Avezaat et al.’s MRI data [6](Figure 6.7).

1.6

1.5 art 1.4 x 1.3 ∆ 1.2 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 0.06

0.05

cap 0.04 x 0.03 ∆ 0.02 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 0.02

0.01 vein

x 0

∆ −0.01 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 80

65 Vol. 60

55 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 Time (sec.)

Figure 6.9: The expansion of intracranial arteries (∆xart) result in venous contraction (∆xvein) and intracranial volume reduction (Vol.) synchronously. Also, the delay of capillary expansion (∆xcap) after arterial expansion. This simulation results agree with Monro-Kellie doctrine and the diagram of phase relationship of blood and CSF from Greitz [61]’s MRI data (Figure 3.4).

110 Lab Data (Canine) 16

ICP 10

7 200 300 400 500 600 700 800 900 1000

120

110

100

50 200 300 400 500 600 700 800 900 1000 ABP(Femoral) Time (200ticks:sec.) Simulation (Human) 14

13.5

12.5

11.5 ICP

10.5

10 1 2 3 4 5 6 105

100

70 1 2 3 4 5 6 ABP(Femoral) Time (sec.)

Figure 6.10: Upper: the timing relationship between arterial blood pressure (ABP) at femoral artery and ICP signal are observed in canine’s experimentation conducted by Cleveland clinic researchers. Lower: the small delay of ABP and ICP signal are predicted from the mathematical model based on human physiology which are in agreement with canine’s monitoring. between heart to intracranial space and heart to femoral artery.

111 6.2 Case of Neurosurgical Disorder

Because cranium is the rigid chambers, an interruption of intracranial space such as an enlargement in volume of intracranial contents brings about the variation of intracranial dynamics. In patients with TBI, a bleeding of cerebral blood vessel referred to intracranial hemorrhage is commonly observed. Intracranial hemorrhage is an abnormal collection of bleeding blood in cranial vault which can cause a mass effect called intracranial mass lesion. An expansion of intracranial mass lesion normally leads to elevated ICP which exerts a collapsing force on intracranial vasculature and brain tissue. Most common type of intracranial mass lesion is hematoma. A formation of hematoma can occupy a finite volume of intracranial space. Intracranial hypertension, reduced cerebral blood flow and brain herniation is common outcome in order to response to the space-occupying intracranial mass lesion. Moreover, an appearance of midline shift on CT scan is typically found in the patients with severe unilateral mass lesion as presented in Figure 2.10(b). Virtually, ICP and cerebral blood flow is bilateral hemisphere balance in healthy individuals. In many clinical reports in patients and animal experimentations with unilateral mass lesion, the difference of ICP between left and right hemisphere (interhemispheric ICP gradients) are observed. For cerebral blood flow, reduced global cerebral blood flow is usually observed in patients who suffer from hydrocephalus and TBI. Moreover, the significantly lower of cerebral blood flow in injured hemisphere than contralateral side are reported in the studies of regional cerebral blood flow. In this mathematical model, studies of the dynamic response related to the size of mass lesion are simulated in two cases: (1) small mass lesion (about 5% of total volume of one hemisphere) and (2) large mass lesion (about 30% of total volume of one hemisphere).

112 6.2.1 Small mass lesion

In case of small mass lesion, volume of small mass (about 5% of total volume of one hemisphere) is placed in the right hemisphere. Interestingly, ICP of lesion side is lower than the non-injured side (left hemisphere) after placing small mass. As shown in Figure 6.11, ICP in normal individuals (dash line) is equal between left and right hemisphere with peaks and dips characteristic pattern of ICP waveform. After a presence of small mass in right hemisphere, the ICP of contralateral hemisphere is higher than normal condition. Moreover, ICP waveform of contralateral side still performs peaks and dips features and synchronization of peak with ICP of normal condition. However, ICP level of injured hemisphere become lower than normal condition. The peaks and dips characteristic pattern of ICP waveform is smoothed out or become dampened ICP waveform. Also, the synchronization of ICP peak value between normal condition and injured hemisphere is distorted.

Intracranial Pressure in Left vs Right Hemisphere 15 Left−ICP Right−ICP ICP at Normal

ICP (mmHg) 10

8 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (sec.)

Figure 6.11: After small mass lesion placing in right cerebral hemisphere, left hemisphere (dark blue) has higher ICP than right hemisphere (green). Dash black waveform represents ICP in normal condition (without mass lesion).

As presented in Figure 6.12, the midline is displaced forward to positive value after intracranial system reaching new equilibrium. It means that the midline shifts forward to the lesion hemisphere after placing small mass. The displacement of midline also

113 Midline Shift 0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

−0.05 Midline Displacement (mm)

−0.1 0 1 2 3 4 5 6 7 Time (sec.)

Figure 6.12: After small mass lesion placing in right cerebral hemisphere, positive displacement of midline refers to midline shift to right hemisphere which has lower ICP. agrees with ICP level between left and right hemisphere which midline shifts to lower ICP side. Cerebral blood flow through intracranial artery in both side of hemisphere is compared as illustrated in Figure 6.13. An appearance of small mass lesion brings about the lower blood flow into intracranial artery of lesion side compared to contralateral hemisphere. For blood flow through contralateral artery (Figure 6.13 (upper)), no significant change of blood flow waveform is found. The less pulsatile outflow with phase shift indicates that buffering function of Windkessel mechanism still performs effectively in non-lesion hemisphere. In contrast, blood outflow after passing intracranial artery of lesion side (Figure 6.13 (lower)) shows the breakdown of intracranial Windkessel mechanism which cannot convert pulsatile blood inflow into less pulsatile outflow to cerebral capillaries. As a result of high pulsatile outflow to capillary bed, it can be indicated that the proportion between arterial expansion and brain expansion become lower in the patient with mass effect. This predicted result also agrees with MRI data in hydrocephalic patient as shown in Figure 3.4(b). Also, smaller phase shift of outflow waveform (reflected wave) after inflow waveform is observed in lesion hemisphere.

114 Left Cerebral Blood Flow 40

−5 3 3.5 4 4.5 5 5.5 6 6.5 7 Right Cerebral Blood Flow 25

0 Flow(ml/s) Flow(ml/s) −5 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (sec.)

Figure 6.13: After small mass lesion placing in right cerebral hemisphere, cerebral blood flow to the right hemisphere (thick green) becomes greatly lower. Also, the high pulsatility with shorter delay of right cerebral blood outflow (thin green) after systolic peak of arterial inflow is observed. However, no significant change of blood inflow (thick dark blue) and outflow waveform (thin dark blue) over left hemisphere is observed.

As presented in Figure 6.14, the observation of systolic expansion of cerebral artery shows that smaller arterial expansion in lesion side compared to the contralateral hemisphere. The phase difference of systolic arterial expansion between lesion and contralateral side are clearly observed. The constriction of cerebral artery in the injured hemisphere leads to increased arterial resistance which decreases arterial compliance. This breakdown of Windkessel mechanism which causes marked reduction of cerebral blood flow, is presented as high pulsatile blood outflow and shorter phase lag between inflow and outflow waveforms on lesion hemisphere. Hence, this predicted results can be used to describe the failure of intracranial volume compensatory mechanism.

6.2.2 Large mass lesion

In this case, large volume of mass (about 30% of total volume of one hemisphere) is still placed in right hemisphere. As presented in Figure 6.15, the predicted ICP of lesion side is higher than contralateral hemisphere in case of large mass lesion.

115 Left vs Right Arterial Expansion 2 Left Arterial Expansion Right Arterial Expansion

1.8

1.6

1.4

1.2

0.8

0.6 Arterial Expansion (mm)

0.4 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (sec.)

Figure 6.14: After small mass lesion placing in right cerebral hemisphere, systolic expansion of artery in lesion hemisphere (green) becomes signiﬁcantly lower compared to non-lesion side (dark blue).

This simulated ICP result agree with the most of clinical case reports in the patient with severe TBI. The predicted ICP waveform of lesion side is flatten out which is similar to the predicted ICP derived from the case of small mass lesion. Hence, the dampened ICP waveform might be used as the indicator of vascular compression in that hemisphere. For large mass lesion, the midline is displaced forward to negative zone after reaching equilibrium as shown in Figure 6.16. It means midline shift over its center line to contralateral side which has lower ICP. This predicted result also agrees with an appearance of midline shift on CT scan commonly observed in patients who suffer from severe hematoma or tumor. As illustrated in Figure 6.17, the significant reduction of cerebral blood flow on both hemisphere after placing large mass lesion, especially, the markedly decreased cerebral blood flow on the lesion hemisphere (Figure 6.17 (lower)) is found. The cessation of cerebral blood flow on the lesion hemisphere after short period of time (about 5 seconds) brings about brain ischemia on that side. This observation enhance that to remove tumor or hematoma promptly after a severe TBI is required, otherwise

116 Intracranial Pressure in Left vs Right Hemisphere 14 Left−ICP Right−ICP

10 ICP (mmHg)

8 9 10 11 12 13 14 15 Time (sec.)

Figure 6.15: After large mass lesion placing in right cerebral hemisphere, left hemisphere (dark blue) has lower ICP than right hemisphere (green). The dampened ICP waveform over lesion hemisphere is also observed.

Midline Shift

0.2

−0.2

−0.4

−0.6

−0.8 Midline Displacement (mm)

−1 0 1 2 3 4 5 6 7 Time (sec.)

Figure 6.16: After large mass lesion placing in right cerebral hemisphere, negative displacement of midline represent the displacement of midline forward to left hemisphere which has lower ICP.

117 Left Cerebral Blood Flow 40

−5 0 1 2 3 4 5 6 7 8 9 10 Right Cerebral Blood Flow 40

0 Flow(ml/s) Flow(ml/s) −5 0 1 2 3 4 5 6 7 8 9 10 Time (sec.)

Figure 6.17: After large mass lesion placing in right cerebral hemisphere, cerebral blood flow to both hemisphere becomes lower. Especially, on the lesion side, blood flow to the right hemisphere (thick green) ceases after 5 seconds. the reduction of cerebral blood flow will further result in secondary brain ischemia and eventually serious neurological disorders. The cerebral blood flow on lesion side is lower than contralateral side which results from the greater restriction of arterial expansion on lesion side as shown in Figure 6.18. This observation is identical to predicted result derived from the case of small mass lesion. The distortion of arterial outflow waveform (Figure 6.17 (Upper)) might be resulted from the displacement of midline to contralateral hemisphere which restricts the arterial expansion as well. As presented in Figure 6.19, the expansion of cerebral capillary is distorted after placing large mass lesion compared to normal condition. The capillary expansion which usually refers to brain expansion are restricted to both hemisphere. Especially, the severe compression of capillary in the lesion hemisphere is presented. This predicted result shows that compression of brain parenchyma called brain herniation after severe TBI can be observed in both hemisphere with more damage on the lesion side.

118 Left vs Right Arterial Expansion

1.8 Left Arterial Expansion Right Arterial Expansion

1.6

1.4

1.2

0.8

0.6

0.4 Arterial Expansion (mm)

0.2 3 3.5 4 4.5 Time5 (sec.) 5.5 6 6.5 7

Figure 6.18: After large mass lesion placing in right cerebral hemisphere, arterial expansion of artery in lesion hemisphere (green) is severely restricted and becomes lower than the expansion of artery in contralateral hemisphere (dark blue).

Left vs Right Capillary Expansion 0.06 Normal Condition Left Capillary Right Capillary

0.055

0.05

0.045

0.04

0.035

0.03

0.025 Capillary Expansion (mm)

0.02 7 7.5 8 8.5 Time9 (sec.) 9.5 10 10.5 11

Figure 6.19: After large mass lesion placing in right cerebral hemisphere, capillary in both hemisphere becomes more restriction compared to normal condition (dash black). Especially, the marked restriction of capillary in lesion hemisphere (green) is observed.

119 6.3 Case of Treatment by using a Medical Balloon

A medical balloon is used as alternative treatment method to make recovery of cerebral blood flow in the patient with neurosurgical condition. In this section, balloon is inserted in the right hemisphere which the side that mass lesion is presented. As shown in Figure 5.9, three different balloon cycles is simulated including augmentation, reduction, and inversion along cardiac cycle. To observe the dynamic response of intracranial system and especially the cerebral blood flow improvement after using medical balloon with intermittent-pumping cycle, both cases of intracranial mass lesion are simulated.

6.3.1 Small mass lesion

After inserting balloon into lesion hemisphere and performing all three balloon cycles, inversion cycle of balloon provides the most improvement of global cerebral blood ﬂow. As shown in Figure 6.20, for the most improvement of cerebral blood ﬂow, the peak of inversion cycle should be synchronous with the peak of initial cardiac output (Figure 6.20 (lower)), not with the peak of ICP waveform.

Inversion vs Cardiac Output 15

Left−ICP 5 Right−ICP Inversion

−5 3 3.5 4 4.5 5 5.5 6 6.5 7 400 Flow after passing Aorta 350 Cardiac Output

300

250

200

150

100

Flow(ml/s) 50

0 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (sec.)

Figure 6.20: Inversion (blue) should do synchronously with cardiac output (thick red) to obtain most cerebral blood ﬂow improvement. ICP response in left (dark blue) and right (green) cerebral hemisphere along inversion cycle are also plotted.

120 Small Mass Lesion Treatment ICP (mmHg)

3.5 4 4.5 5 5.5 6 3.5 4 4.5 5 5.5 6 Time (sec.) Time (sec.)

Figure 6.21: Intracranial pressure in left Figure 6.22: Intracranial pressure in left (dark blue) and right (green) hemisphere (dark blue) and right (green) hemisphere with small mass lesion after inversion treatment

As shown in Figure 6.22, the ICP waveform of non-lesion side (left hemisphere) after inversion treatment is similar to ICP waveform with in the case of small mass lesion (Figure 6.21). However, the dampened ICP waveform of the lesion side (right hemisphere) is likely transformed into peaks and dips ICP waveform after inversion cycle of balloon. In non-lesion hemisphere, arterial blood inflow/outflow waveform in case of small mass lesion (Figure 6.23 (upper)) and during inversion treatment (Figure 6.24 (upper)) are almost identical. However, the inversion cycle can increase arterial blood inflow to lesion hemisphere with undesirable high pulsatile outflow as shown in Figure 6.24 (lower). The comparison of arterial expansion in both hemispheres between case of small mass lesion and after inversion treatment is presented in Figure 6.25 and Figure 6.26 respectively. Inversion cycle of balloon which is synchronous with the initial cardiac cycle provides the additional expansion of artery on the lesion hemisphere. Furthermore, the larger arterial lumen diameter can decrease the flow resistance which allows additional blood flow to intracranial space. As presented in Table 6.1, average value of ICP, cerebral blood flow (Qbrain) and

121 Left Cerebral Blood Flow Left Cerebral Blood Flow Flow(ml/s) 3.5 4 4.5 5 5.5 6 3.5 4 4.5 5 5.5 6 Right Cerebral Blood Flow Right Cerebral Blood Flow Flow(ml/s) 3.5 4 4.5 5 5.5 6 3.5 4 4.5 5 5.5 6

Figure 6.23: Cerebral blood ﬂow to the left Figure 6.24: Cerebral blood ﬂow to the left (thick dark blue) and right (thick green) (thick dark blue) and right (thick green) hemisphere with small mass lesion hemisphere after inversion treatment

Small Mass Lesion Treatment

Left Arterial Expansion Right Arterial Expansion Arterial Expansion (mm)

3.5 4 4.5 5 5.5 6 3.5 4 4.5 5 5.5 6 Time (sec.) Time (sec.)

Figure 6.25: Expansion of left cerebral Figure 6.26: Expansion of left cerebral artery (dark blue) and right (green) cere- artery (dark blue) and right (green) cerebral artery with small mass lesion bral artery after inversion treatment

122 Table 6.1: Comparison table of ICP, cerebral blood ﬂow (Qbrain) and ﬂow to hands (Qhand) during normal condition, with small mass lesion and after inversion treatment

blood flow to hand (Qhand) during normal condition, with small mass lesion, and after inversion treatment are compared. The percentage change column represents the percentage difference between the case of mass lesion and after treatment by inversion cycle. As mentioned earlier in case of small mass lesion, average ICP of non-lesion hemisphere (ICP,L) becomes higher and lesion hemisphere (ICP,R) becomes lower compared to normal condition. After inversion treatment, the small increase in ICP of lesion hemisphere brings about the small increase in total ICP (L+R/2). Moreover, a presence of small mass lesion results in marked reduction of cerebral blood flow to lesion hemisphere (Qbrain,R) which leads to decreased global cerebral blood flow (L+R/2). The inversion cycle of balloon can significantly increase cerebral blood flow on lesion side about 21.6% improvement which can improve global cerebral blood flow by 6%. However, the inversion treatment cannot recover cerebral blood flow to normal condition. Since the mathematical model assumes that blood will flow to the hand if blood cannot flow into the intracranial space, the amount of blood flows to each hand and each intracranial hemisphere has inversely proportional relationship.

123 Inversion vs Cardiac Output 15

Left−ICP 5 Right−ICP Inversion

−5

−10

−15 11 11.5 12 12.5 13 13.5 14 14.5 15 400 Blood Flow After Passing Acsending Aorta 350 Cardiac Output

300

250

200

150

100

50 Flow(ml/s) 0 11 11.5 12 12.5 13 13.5 14 14.5 15 Time (sec.)

Figure 6.27: Inversion (blue) should do nearly synchronously with cardiac output (thick red) to obtain most cerebral blood ﬂow improvement. ICP response in left (dark blue) and right (green) cerebral hemisphere along inversion cycle are also plotted.

6.3.2 Large mass lesion

Similarly, from all of balloon cycles perform in large mass lesion case, the most improvement of cerebral blood flow is also provided by inversion cycle of balloon. In this case, however, the peak of inversion cycle is not precisely synchronous with the peak of initial cardiac cycle. As shown in Figure 6.27, the small delay of inversion cycle after initial cardiac cycle brings about the most cerebral blood flow improvement for the case of large mass lesion. In addition, ICP response for large mass lesion (Figure 6.28) is compared to the case of inversion treatment by using a medical balloon (Figure 6.29). After inversion treatment, the ICP waveform of non-lesion side (left hemisphere) is converted to wider pulse and higher ICP level. On lesion side (right hemisphere), the predicted ICP waveform is converted from flatten-out waveform to larger ICP pulse along inversion cycle of balloon. In case of large mass lesion, blood flow into both intracranial arteries is decreased. Especially, the lack of blood supply into the lesion hemisphere as presented in Figure 6.30 (lower). After balloon insertion (Figure 6.31), inversion cycle can increase blood

124 Large Mass Lesion Treatment ICP (mmHg)

10 11 12 13 10 11 12 13 Time (sec.) Time (sec.)

Figure 6.28: Intracranial pressure in left Figure 6.29: Intracranial pressure in left (dark blue) and right (green) hemisphere (dark blue) and right (green) hemisphere with large mass lesion after inversion treatment

flow to both hemispheres which recovers blood supply on the lesion hemisphere from loss of blood flow to continuous flow. However, high pulsatile outflow to capillary bed is observed which is unfavorable condition. In Table 6.2, the existence of large mass lesion results in an increase of ICP level on the lesion side (ICP,R) over the non-lesion hemisphere (ICP,L). Cerebral blood flow on both hemispheres (Qbrain) are reduced significantly in the case of large mass lesion. Furthermore, the cessation of blood supply to lesion hemisphere (Qbrain,R) is also observed. Inversion treatment can greatly improve blood flow on lesion side which gain 94% improvement of global cerebral blood flow (L+R/2). However, cerebral blood flow is still far from normal condition.

125 Left Cerebral Blood Flow Left Cerebral Blood Flow Flow(ml/s) 6.5 7 7.5 8 8.5 9 11.5 12 12.5 13 13.5 14 Right Cerebral Blood Flow Right Cerebral Blood Flow Flow(ml/s) 6.5 7 7.5 8 8.5 9 11.5 12 12.5 13 13.5 14

Figure 6.30: Cerebral blood ﬂow to the left Figure 6.31: Cerebral blood ﬂow to the left (thick dark blue) and right (thick green) (thick dark blue) and right (thick green) hemisphere with large mass lesion hemisphere after inversion treatment

Table 6.2: Comparison table of ICP, cerebral blood ﬂow (Qbrain) and ﬂow to hands (Qhand) during normal condition, with large mass lesion, and after inversion treatment

126 6.4 Discussion

To convert the pulsatile nature of blood flow created by pumping action of heart into less pulsatile and continuous outflow to capillary bed is major function of Windkessel mechanism. This buffering function is mainly provided by the elasticity of artery and flow resistance which has different physiological properties in various parts of arterial system. In this mathematical model, the dynamical relationship of blood flow, pressure and vascular expansion in human major arterial system and intracranial system is studied based on Windkessel mechanism. For normal condition, the effective Windkessel mechanism not only provides the arterial blood outflow with less pulsatility but the phase shift after inflow waveform is also another characteristic feature. The predicted results have well agreement with clinical data in many aspects such as pulsatile waveform and phase relationship in both major arteries to lower limbs and intracranial space. In addition, the simulation reveals the time delay of arterial blood pressure at femoral artery which usually selected as site of blood pressure monitoring after ICP signal. For intracranial space, the dynamic of intracranial contents is also based on Windkessel mechanism under the constraint of Monro-Kellie doctrine. Arterial blood inflow with delay of systolic expansion of arteries is the major source to drive out the intracranial dynamics. Systolic expansion of intracranial arteries which synchronous with arterial outflow leads to ICP pulsation, venous contraction and delay of capillary dilation. Moreover, bilaterally interhemispheric balance of ICP and cerebral blood flow are normally observed in healthy individuals. For neurosurgical condition, this mathematical model demonstrates the change of intracranial dynamic secondary to the mass effect condition. Furthermore, the simulation results show that different size of mass lesion lead to vastly different intracranial dynamics response. Especially, the interhemispheric asymmetry of ICP and cerebral blood flow between lesion and non-lesion hemisphere is observed in term of level and waveform. An appearance of large mass lesion brings about the higher of ICP on

127 the lesion hemisphere compared to contralateral side (and vice versa in case of small mass lesion). In response to the interhemispheric ICP gradient, midline shifts forward over center line to the lower ICP hemisphere. In my opinion, interhemispheric ICP gradient may not be observed if no blockage of subarachnoid space as mentioned by Langfitt et al. [92, 94]. However, most case of severe neurosurgical disorders are associated with the blockage CSF flow and pressure communication pathway which follow by the interhemispheric imbalance of ICP. In addition, peaks and dips ICP waveform of the lesion hemisphere is flatten out into dampened ICP waveform. For cerebral blood flow, a presence of mass lesion results in the reduction of global cerebral blood flow and a marked reduction of regional blood flow also on the lesion hemisphere. Arterial blood outflow waveform shows the higher pulsatility and shorter phase lag after inflow waveform. Also, a larger size of mass lesion leads to greater reduction of regional and global cerebral blood flow. Hence, it can be concluded that the interhemispheric ICP gradients and reduction of global and regional cerebral blood flow depend on the size of mass lesion which agree with many animal experimentation and clinical case reports. Moreover, the observation of the arterial expansion shows that reduction of CBF results from the smaller expansion of arterial lumen diameter. As a result of restriction of arterial expansion, flow resistance is increased which reduces arterial volume compensatory capacity (arterial compliance). This situation can explain the failure of intracranial Windkessel mechanism that the pulsatile energy from cardiac output cannot be filtered into nearly pulseless outflow. According to simulation results, many observations can be used as the indicator to predict the failure of intracranial Windkessel mechanism which is highly useful for real-time patient monitoring. Higher amplitude of arterial outflow and venous outflow compared to healthy individuals is the fundamental indicator that artery cannot convert pulsatile inflow into steady outflow. Also, the smaller difference in amplitude between arterial inflow and outflow or venous outflow can be another indicator by using blood flow waveform. In the patient with space-occupying lesion, the reduction of cerebral blood flow due to the restriction of artery is typically found. However,

128 because of high pulsatile arterial outflow, capillary expansion which provided by the arterial outflow is still relatively high compared to arterial expansion. In other words, the lower proportion between arterial expansion and capillary expansion (usually referred as brain expansion) indicates the problem of Windkessel buffering function. Moreover, the shorter phase lag between the peak of arterial blood inflow and arterial outflow is commonly observed in the patient with Windkessel mechanism problem. For practical monitoring, arterial outflow might be replaceable by capillary outflow, venous outflow, or ICP signal because they perform almost identical timing. Nor- mally, the ICP waveform perform peaks and dips feature. Dampened ICP waveform might be used to indicate the compression of vascular bed and brain herniation in that hemisphere. The breakdown of Windkessel mechanism also relates to cardiac afterload as mentioned in Section 3.1. The failure of volume compensatory mechanisms usually result in high pulsatility and much earlier venous return to heart which can increase work load of the heart. High systolic blood pressure and blood flow velocity are responded to increased heart afterload. In the future, the cardiac action that respond to the change of venous return might be included in the mathematical model. Hence, the change of arterial blood pressure at femoral artery and peak-to- peak difference in timing of blood flow or ICP might be used as another indicator to respond to the change of blood pressure and flow velocity respectively. The simulation results show that the intermittent action of medical balloon can improve the cerebral blood flow in patient with decreased cerebral blood flow due to mass effect. Inversion cycle is the only technique that can improve CBF and should operate approximately at the same time with the peak of initial cardiac output. However, the high pulsatility arterial blood outflow to capillary bed is an undesirable result. More- over, cerebral blood flow cannot be restored to normal level because balloon insertion also occupies the finite volume of intracranial space. Hence, the technique to recover cerebral blood flow by balloon insertion might not be recommended to the patient who already loads with intracranial space occupation or decreased intracranial compliance. To make recovery of cerebral blood flow and volume compensatory capacity,

129 Occlusion/Vasospasm

Reduction of Cerebral Blood Flow

NPH Breakdown of Windkessel Mechanism Reduction of Reduction of Arterial Expansion Capillary Expansion

TBI Mass Eﬀect

Reduction of Reduction of Squeezing force Squeezing force Ventricular Enlargement at Choriod Plexus at Venticles (Hydrocephalus)

Collection of CSF in Ventricles

Obstructive Hydrocephalus

Figure 6.32: Developmental cycle of hydrocephalus surgical treatment or shunting placement is still a practical solution. However, the balloon might be used for a short period of time to stimulate cerebral blood flow in the patient with extremely low cerebral blood flow after lesion removal. Furthermore, the medical balloon might be conjointly used during surgical shunting because shunting can provide a little extra space to compensate for the space occupied by balloon. This mathematical model is one of the useful tool to predict a possible outcome of patients who suffer from the failure of volume compensatory mechanisms due to space- occupying mass lesion. Moreover, I believe that the enlargement of cerebral ventricles referred to hydrocephalus might be considered as the mass effect because the enlargement of ventricles also occupy the finite volume of intracranial space. Especially, the

130 behavior of unilateral dilation of ventricle (called unilateral or monoventricular hydrocephalus) as presented in Figure 2.13 might be able to understand from the simulation results of unilateral mass lesion. In my opinion, the cause of hydrocephalus might be described as the malfunction of intraventricular CSF flow due to the abnormalities of intracranial dynamics. As mentioned earlier, the systolic expansion of arteries is the major source to drive out the intracranial dynamics and intraventricular CSF flow. Also, choroid plexus is the major site of CSF formation and stimulate the pulsatile CSF flow in ventricular system induced by systolic arterial expansion. Hence, the intraventricular CSF flow requires two consecutive squeezing forces provided by arterial and capillary expansion which can be divided into two stages. For the first stage, the large systolic expansion of artery will squeeze choroid plexus to drive out the CSF flow. For the second stage, the small expansion of capillary provides the additional force on lateral ventricles for CSF flow to the third and fourth ventricle and then to SAS. The development of hydrocephalus might be expressed as the inadequate of squeezing force exerting on choroid plexus and ventricles which can be explained in the aspect of developmental cycle as illustrated in Figure 6.32. The developmental cycle of hydrocephalus shows that any abnormalities in the cycle can be the cause that will develop to hydrocephalus. For example, the marked reduction of cerebral blood flow which may result from vascular occlusion or vasospasm decrease the pulsatile volume of blood into the cranium and reduce the expansion of intracranial artery and capillary. Also, the effective timing to compress the choroid plexus and ventricles is distorted due to the phase shift of vascular expansion especially capillary. Thus, the squeezing force that drive out CSF to SAS cannot be provided sufficiently. When the CSF cannot be squeezed out from the ventricles, the accumulation of CSF within ventricle might be occurred. If the treatment is not provided, the collection of CSF will dilate the ventricles. Furthermore, the ventricular enlargement can be considered as the mass effect by occupying the intracranial space. After that, the volume compensatory capacity will be exhausted and the Windkessel mechanism will be break-downed. The failure of Windkessel mechanism will further reduce the cerebral

131 blood flow and then proceed into the cycle. The enlargement of ventricle affects the intracranial Windkessel mechanism in two aspects. First, ventricle dilation occupies the intracranial space which can be considered as the mass effect as mentioned above. Second, the compression of elastic ventricles is normally provided by the expansion of capillary. Hence, the enlargement of ventricles not only resists the expansion of capillary but also leads to the loss of absorbing function of ventricles which normally acts as one of pulsatile absorber in the intracranial space. As a result, the breakdown of intracranial Windkessel mechanism is developed. The developmental cycle of hydrocephalus also can be used to classify the cause of hydrocephalus due to other factors. For example, the ventricular obstruction of CSF flow pathway referred to obstructive hydrocephalus brings about the collection of CSF in ventricles. An appearance of brain hematoma observed in the patients with TBI can be classified as hydrocephalus secondary to head injury which considered as the mass effect. Moreover, the development of NPH in the elderly as the result of aging or arteriosclerosis might be explained by the gradual loss of arterial compliance which restricts arterial expansion and eventually causes the failure of Windkessel mechanism. Also, the blockage of CSF flow pathway for communication between intracranial SAS and compliant spinal theca in lumber region can be considered as the breakdown of Windkessel mechas- nism in the developmental cycle because of the loss of volume compensatory capacity. Hence, to study the effect of ventricular dynamic on intracranial system related to the development of hydrocephalus, the ventricular system should be included in the mathematical model in the future. According to the developmental cycle of hydrocephalus, the treatment of hydrocephalus should focus on preventing or breaking up the cause of development. For example, to remove the space occupying mass lesion by surgery is the practical approach for the patients with TBI. In the patients with NPH who require the improvement of arterial compliance, vasodilating drug might be the suitable choice for restoring arterial compliance. Shunting is still the appropriate treatment procedure to recover the intracranial volume compensatory capacity which may either result

132 from the intracranial occupation due to mass effect or the blockage of CSF flow pathway between intracranial and compliant spinal SAS. To remove the collection of CSF in lateral ventricles, an endoscopic third ventriculostomy (ETV) by bypassing CSF from the third ventricle flow directly to SAS might be the most effective solution. Ca- dence action of the medical balloon is another treatment option for hydrocephalus. As shown in the simulation results, the inversion cycle of balloon can increase the pulsatile volume of cerebral blood provided by the greater expansion of artery. A sufficient arterial expansion will provide the capable force acting on choroid plexus for the intraventricular CSF pulsation. Furthermore, the augmentation cycle directly exerted the squeezing power on choroid plexus might be the alternative therapy to treat hydrocephalus which requires further studies. However, the insertion of balloon inside intracranial space may occupy the finite volume of cranium. The collaboration of shunting while the balloon is in use may eliminate this space occupying problem.

133 Chapter 7

Summary and Conclusions

7.1 Summary

In this dissertation, by simulating through the mathematical model, the high pulsatile nature of blood flow major human arterial system can be converted into less pulsatility which results from the effectiveness of Windkessel mechanism. The Windkessel mechanism is provided by the buffering function obtained from vascular elasticity and flow resistance. For intracranial space, not only the vascular elasticity acts as pulsatile absorber but the intracranial compliance which defined by volume compensatory mechanism also together provides compliance to overall intracranial system. The interactive relationship among major intracranial contents is presented. This observation clarifies the intracranial system in term of dynamics along the cardiac output which pulsatile arterial blood flow is the major driving force. Also, the demand and compensation in volume of intracranial contents according to Monro-Kellie doctrine is well satisfied. An appearance of unilateral mass lesion brings about the variation of intracranial dynamics because the mass lesion occupies the finite volume of intracranial space. Especially, the interhemispheric asymmetry of intracranial pressure (ICP) and cerebral blood flow are presented. Also, the displacement of midline (midline shift) is observed. The predicted show that higher ICP would be on either the lesion or non-

134 lesion hemisphere depends on the size of mass lesion. However, cerebral blood flow of the lesion side is always lower than the contralateral side because of the collapsing of cerebrovascular bed. In term of waveform and timing, the significantly interhemispheric different of signals is also observed. This can be used to categorize between the normality and abnormality of intracranial Windkessel mechanism using signal analysis. For useful of real-time patient monitoring, many observations can be used as the indicator to predict the failure of intracranial Windkessel mechanism including waveform, amplitude, timing and phase shift. To hypothesize the cause of hydrocephalus, the failure of intracranial Wind- kessel mechanism might be the good explanation especially for communicating hydrocephalus. However, I believe that the failure of intracranial Windkessel mechanism can be both cause and result of hydrocephalus. Neurosurgical disorders are typically related to decreased cerebral blood flow. In order to recover cerebral blood flow, the medical balloon insertion with intermittent action is used as the alternative treatment method. According to the simulation results, the inversion action of balloon can increase the cerebral blood flow by increasing the arterial expansion. For the most improvement, the inversion cycle should do approximately synchronously with the initial cardiac output. However, cerebral blood flow cannot be restored to normal level because balloon insertion also occupies the intracranial space. Thus, the balloon might be recommended to use for a short period of time to stimulate cerebral blood flow in the patient with extremely low cerebral blood flow after lesion removal or conjointly used with shunting to provide the extra space to compensate for the space occupation of balloon This pulsatile mathematical modeling is the useful tool to understand the hemodynamics and intracranial system based on Windkessel mechanism. In addition, improved understanding of its mechanism and abnormalities can help to explore the cause and effect of intracranial disorders. This observation can also enlighten the medical professionals to direct future protection and treatment strategies against this related clinical condition properly.

135 7.2 Recommendations for Future Development

The following list contains feasible development for the further studies:

• Investigation on the eﬀect of another neurosurgical conditions on intracranial system

• Addition of ventricular system into model to study the dynamics of ventricular system and to investigate the dilation of ventricles in the patients with hydrocephalus

• Incorporation of cardiac response to the dynamical change of intracranial system such as the earlier return of venous ﬂow due to decreased intracranial compliance

• Simulation of the alternative treatment method to improve cerebral blood ﬂow or restore eﬀectiveness of intracranial Windkessel mechanism

136 Appendix A

Parameters for the Model of Hemodynamics and Intracranial System

Table A.1: Parameters for the Model of Hemodynamics and Intracranial System

Parameter value −5 Dynamic viscosity of blood, µblood (kg/cm.s) 10 3 Density of blood, ρblood (kg/cm ) 0.001 Heart rate, ω (rad/s) 2.3π - 2.4π Radius of intracranial artery’s outlet, xout (cm) 0.5 Total volume of left hemisphere, VL (ml) 75 Total volume of right hemisphere, VR (ml) 75 2 Cross-sectional area of midline, Amid (cm ) 15 2 Midline tissue’s stiﬀness, kmid (kg/s ) 1000 Mass of midline, mmid (kg) 0.1 Volume of small mass lesion, Vlesion,S (ml) 4 Volume of large mass lesion, Vlesion,L (ml) 25 Initial radius of blood vessel, x0,vessel (cm) Ascending aorta 1.5 Descending aorta 1.2 Common iliac artery 1 External iliac artery 0.7 Femoral artery 0.5 Common carotid artery 1.2

137 Table A.1: Parameters for the Model of Hemodynamics and Intracranial System

Parameter value Subclavian artery 1 Intracranial artery, x0,art 0.7 Intracranial capillary, x0,cap 0.2 Intracranial vein, x0,vein 1 Length of blood vessel, lvessel (cm) Ascending aorta 15 Descending aorta 40 Common iliac artery 30 External iliac artery 10 Femoral artery 20 Common carotid artery 25 Subclavian artery 25 Intracranial artery 3 Intracranial capillary 5 Intracranial vein 5 2 Stiﬀness of blood vessel, kvessel (N/m, kg/s ) Ascending aorta 1800 Descending aorta 2300 Common iliac artery 2500 External iliac artery 2300 Femoral artery 2000 Common carotid artery 2500 Subclavian artery 1600 Intracranial artery, keq,art 600 Intracranial capillary, kcap 1000 Intracranial vein, keq,vein 800 Pressure in blood vessels outlet, Pout (mmHg) Ascending aorta 85 Descending aorta 80 Common iliac artery 80 External iliac artery 60 Femoral artery 60 Common carotid artery 80 Subclavian artery 80 Intracranial artery, keq,art 40 Intracranial capillary, kcap 25

138 Table A.1: Parameters for the Model of Hemodynamics and Intracranial System

Parameter value

Intracranial vein, keq,vein 15

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