臺灣博碩士論文加值系統

評估心血管特徵和相連的終端器官健康狀態，目前臨床仍然缺乏可靠和非侵入式的診斷工具。本論文旨在發展一套識別程序，以一維波傳播模型為建構基礎，來估算個人的血液動力參數。識別方法解決了血液動力學的逆問題，得到臨床上有興趣的模型參數估算值。動脈硬度(Arterial Stiffness)、無壓力腔半徑(Stress-free Lumen Radius)以及末端區塊參數(Terminal Lumped Parameters)，皆由本方法估算獲得。
參數估計程序使用臨床可量測數據作為系統的輸入和觀察，基於不考慮數據誤差和測量不確性。識別方法包含一維流狀態估測和基因演算參數搜尋法，因此物理參數和狀態估測皆同時包括在識別程序中。採用差分進化法(Differential Evolution)來優化模型參數，並以平行運算來加速計算時間。為了能應付在體內獲得的不同測量數據，本研究提出和建構三種識別方法，分別使用壓力-流量(pq)、壓力-速度(pU) 、直徑-速度(DU)的波形作為系統輸入/測量的數據。
在一維的血液動力模擬中，本研究已發展出高解析Roe數值法(Roe's Scheme)及特徵邊界條件(Characteristic Boundary Conditions)，來求解存在於心血管流問題中的複雜波反射現象。使用模擬的數值或臨床的數據來做驗證，分別估測局部血管和末端器官參數，其目的在於評估本方法的可行性和準確性。
結果顯示這三個識別方法是準確和可行的，其中DU法在逐點測定上特別準確，延伸了血管超音波檢查(Vascular Ultrasonography)的可用性。再者，使用體內所測量到的數據，以pq法估算個人的手臂動脈網絡參數，得到可接受的匹配結果。此外，使用肱動脈壓力/血管壁擴張波形來識別末端器官參數，其可行性已經實現。這些初步結果顯示，在此模型本位識別方法的助益下，使用週邊動脈可測量的數據，以非侵入性的方式來診斷個人器官的健康狀態，在理論上是可行的。

A reliable, non-invasive diagnostic tool for assessing cardiovascular characteristics and/or the connected end organ health state is still lacking. The present work aims at developing an identification procedure for estimating individual hemodynamic parameters based on a one-dimensional (1-D) tree-like vascular flow model. With the use of clinically available measurements, the proposed identification methods solve the hemodynamic inverse problem associated with the modeled vascular system, yielding the estimates of the unknown model parameters that are of clinical interest. For the present vascular diagnostic method, the arterial stiffness and stress-free lumen radius as well as the terminal lumped resistances and compliance that reflect the health state of the connected end organs were estimated.
The present parameter estimation procedure uses measurable clinic data as system input and observation functions. Sensor data errors and measurement uncertainties are not considered. The measurements obtained at sites of interest are assumed noise-free and mutually compatible. The present identification procedure consists of a 1-D flow state estimator and a genetic parameter search algorithm, and thus both physical parameters and state estimation are included simultaneously in the identification procedure. Differential evolution (DE), a global genetic search algorithm, has been employed as the parameter optimizer. Parallel computing was applied to accelerate the speed of DE optimization. To cope with different data measurements obtained in vivo, identification methods that use pressure-flow rate (pq), pressure-velocity (pU), and diameter-velocity (DU) waveforms as system input/measurement pair were proposed and constructed.
The present model-based identification algorithm was constructed and validated using a numerical 1-D hemodynamic simulation code which simulates pulsatile blood flow circulating in human arterial system with high-fidelity. In this simulation code, a high-resolution Roe’s scheme augmented by characteristics-based boundary condition treatments were developed to solve the complex wave reflection and re-reflection phenomena prevailing in the tree-like vascular network. Validations were performed on estimating regional vascular and terminal end-organ parameters, respectively, using both numerical and clinical data pairs to assess the feasibility and accuracy of the proposed identifier. The results show that all the three pq, pU and DU identification methods are accurate and feasible. For point-wise vascular diagnosis, the DU method has been particularly accurate, which may potentially extend the current usability of vascular ultrasonography onto a new horizon of evaluating local arterial stiffness non-invasively. For identifying individual parameters pertaining to a segmental arterial network of an arm, agreed hemodynamic waveforms reconstructed by the pq method were compared favorably to the in vivo measurements. Furthermore, the feasibility of identifying end-organ hemodynamic parameters using brachial (peripheral) pressure/wall distension waveforms was demonstrated. These preliminary successes indicate that, with the aid of model-based identification, a non-invasive, individual-based diagnosis of the organ health states using measurable observations at peripheral arteries is theoretically possible.

ABSTRACT IN CHINESE i
ABSTRACT x
ACKNOWLEDGEMENTS xiii
CONTENTS xiv
LIST OF TABLES xviii
LIST OF FIGURES xix
NOMENCLATURE xxiii
CHAPTER I INTRODUCTION 1
1.1 Cardiovascular physiology and pathology 3
1.1.1 Systemic arteries 3
1.1.2 Arterial walls 4
1.1.3 Blood flow and pressure 5
1.1.4 Aging of arteries 6
1.2 Arterial stiffness and assessment methods 7
1.2.1 Distensibility method 9
1.2.2 Pulse wave velocity method 10
1.2.3 Single-point wave speed assessment 11
1.3 Modeling of physiological flows 12
1.4 Inverse modeling approach 13
1.5 Aims of this thesis 16
1.6 Thesis outline 16
CHAPTER II MATHEMATICAL MODEL AND NUMERICAL ALGORITHMS 18
2.1 1-D flow formulation 18
2.2 Characteristic form 20
2.3 Flux-difference splitting 22
2.4 Spatial discretization 24
2.5 Flux limiter 24
2.6 Time marching 25
CHAPTER III BOUNDARY CONDITION TREATMENTS 27
3.1 Time-dependent numerical boundary equations 28
3.2 Boundary conditions 29
3.2.1 Nonreflecting boundary condition 30
3.2.2 Closed-end boundary condition 30
3.2.3 Open-end boundary condition 31
3.2.4 Partially reflecting and general formalism of boundary conditions 31
3.2.5 Physical meaning of reflection coefficient 33
3.2.6 Comparison of proposed and classical reflection coefficient definitions 34
3.3 Bifurcation condition treatment 35
3.3.1 Interface conditions 35
3.3.2 Physical interpretation of reflection coefficient at bifurcation 37
3.4 Physiologically relevant terminal Windkessel models 38
3.4.1 Single resistance (R) model 39
3.4.2 Two-element (CR) Windkessel model 40
3.4.3 Three-element (RCR) Windkessel model 41
CHAPTER IV PARAMETER IDENTIFICATION PROCEDURE 44
4.1 Data acquisition and validation 45
4.1.1 Data acquisition 45
4.1.2 Sensor data validation 47
4.2 System input and observer functions 48
4.3 Model parameter initialization and reduction 48
4.4 Least-squares estimation 50
4.5 Differential evolution (DE) algorithm 51
4.5.1 Initial population 52
4.5.2 Mutation 52
4.5.3 Crossover 53
4.5.4 Selection 53
4.5.5 Optimization example 54
4.6 Parallel computing 55
CHAPTER V SCHEME VALIDATION 56
5.1 Example 1: test case with discontinuous flow 57
5.2 Example 2: reflecting boundary condition 58
5.3 Example 3: numerical dissipation 60
5.4 Example 4: a tree-like vascular network model 61
5.5 Closure remarks on high-resolution Roe scheme 62
CHAPTER VI PARAMETER IDENTIFICATION FOR HUMAN ARTERIAL NETWORK MODEL 64
6.1 Arterial network model 64
6.2 Sub-model parameter estimation using numerically generated data 66
6.2.1 Single-point approach 66
6.2.2 Multiple-point approach 68
6.3 Sub-model parameter estimation using in vivo data 69
6.4 End-organ parameter estimation using peripheral measurements 71
6.5 Clinical relevance and limitation 73
CHAPTER VII CONCLUDING REMARKS 76
7.1 Conclusions and clinical relevance 76
7.2 Limitations and recommendations 78
REFERENCES 79
APPENDIX A 93
TABLES 97
FIGURES 112
PUBLICATION LIST 159
VITA 160

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