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View of Physiology 11 2.1 Thecardiovascularsystem MATHEMATICAL MODEL FOR HEMODYNAMIC AND INTRACRANIAL WINDKESSEL MECHANISM by 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 ________________________________________________ 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 projec- tions 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 ven- tricles 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 cere- bral 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 tomogra- phy 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 cere- bral aqueduct (arrow) is patent and there is no evidence of obstruction within the ventricular system. This is a case of communicating hydro- cephalus[28]. ............................... 34 2.12 Cerebral blood flow in (a) healthy individuals and in (b) communicat- ing hydrocephalus. (a) The arterial windkessel mechanism, the wide intracranial vessels with small vascular resistance and the venous out- flow 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 “wa- terfall phenomenon”, i.e. the pressure drop occurring from the cortical veins to the venous sinus. (b) In communicating hydrocephalus, the in- creased transmantle pulsatile stress (i.e. difference in pressure between ventricle and subarachnoid space) and the ventricular dilation com- presses 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 hy- drocephalus due to shunt overdrainage: marked dilatation of the left lateral ventricle (b) MRI performed 10 days after the endoscopic fen- estration 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 pe- ripheral 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 veloc- ity increases and
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