臺灣博碩士論文加值系統

下肢週邊血管疾病 (週血管病；PAD) 是一種很普遍但又隱密不易診斷的疾病，主要是由動脈粥樣硬化血管內壁所造成，導致動脈閉塞而下肢壞疽。週血管病最主要的危險因子是第二型糖尿病，老化，和吸煙，但是其他包括高血壓、高膽固醇、和高同型半胱氨酸血症等也會增加週血管病的風險。
大部分病人和醫師都不太了解週血管病，因此延遲診斷和治療並非少見。這種疾病的典型臨床表現為間歇性跛行和休息時的腿痛，但有的是以糖尿病足、感染蜂窩性組織炎、或骨髓炎為最初的臨床表現。無論何種表徵，週邊血管觸診異常否，動脈阻塞程度仍無法精確得知；唯有依據傳統的、電腦斷層、或磁振造影的血管攝影術方知下肢的那些血管阻塞。但在臨床表現之前，即使是有上述危險因子的，也無從了解自己是否罹患週血管病。延遲診斷的原因之一其是缺乏早期診斷的篩檢和診斷工具，當然也就無法積極監測週血管病的發展和治療的效果。在區域醫院和醫學中心因為具有血管攝影的設備，晚期和危及下肢的週血管病可以使用經皮血管形成術疏通阻塞。
但是在無症狀期，目前只有杜普勒超音波和踝肱動脈血壓指數可以診斷週血管病。踝肱脈壓指數的弱點是操作不易、本質上易生誤差、和無法使用於相當程度硬化的血管；尤其是最後一項，更是他的致命傷，因為許多年長者、尿毒症和高血壓患者的下肢動脈是有嚴重的鈣化。即便如此，當前國際上的週血管病診斷參考標準，仍然是踝肱脈壓指數。這個方法把週血管病的嚴重程度分為正常、低度、和高度三種，根據各自的指數為 ≧ 0.9、(0.9， 0.5]、和 〈 0.5。
光體積描計法 (photoplethysmography; PPG) 是一種光學的、非侵入性的技術，可以量測人體組織的血容量變化。目前臨床上被廣泛地應用於測量周邊血氧的飽和度合和心臟律動的相關參數。研究報告顯示週血管病患者因為長期的左右腳之間不等速的阻塞，造成兩腳之間的光體積波之傳輸時間差比健康人統計上有明顯的增長，非常具有診斷的價值。然而當代醫學仍舊缺乏診斷週血管病的光體積描計器。
這篇論文的首要目的是開發電腦輔助的診斷儀器以幫助週血管病的早期診斷和追蹤評估。第一個試驗是利用光體積描計器結合分數階混沌同步所建構的動態誤差和分類技術，紀錄25個健康的成年人和有週血管病的糖尿病人的光體積描計信號。這11名健康成年人和14例糖尿病患者，依據踝肱血壓指數區分週血管病的嚴重程度為正常、低度、和高度三種。參考心電圖R波計算 △PTTPp、△PTTf和△RT三種參數，並應用陳李氏混沌系統計算其分數階動態誤差。之後再應用彩色模型(Hue-Saturation-Value) 進行彩色關係分析 (color relational analysis)，精準有效地的執行這三種週血管病嚴重度的分類。
在第二個試驗中，總共紀錄15名健康人及17例糖尿病而且有週血管病的患者進行光體積描計信號。這次的分類採用支持向量機 (support vector machine) 作為分類器，並且進行狼群搜索 (wolf pack search) 最佳化以取得必要的參數。也是精確有效地完成分類。比較人工神經網絡和其他機器學習技術，這兩種方法需要的參數、訓練時間、訓練資訊量、和統計複雜性都比較少，而且參數的調整也比較不會落入區域性極值的圈套。因此，發展一套以光體積描計法為基礎的週血管病電腦輔助診斷系統是非常具有潛力的。
光體積描計法為基礎的週血管病電腦輔助診斷系統結合彩色關係分析法和支持向量機分類技術是有可能幫助早期診斷和病程追蹤週血管病的。這樣的系統不必添加心電圖，方便攜帶，又具有即時性和準確性的優點。總之，光體積描計法的訊號經由分數階微分和陳李氏混沌同步化而建構成的動態誤差系統，再結合機器學習理論的技術如結合彩色關係分析法和支持向量機分類技術，極具發展診斷週血管病輔助工具的潛在價值，尤其是在社區、診所、和地區醫院篩選和追蹤糖尿病等高危險群，以達有效地監控週邊血管病和減少截肢的目標。

Lowe-limb peripheral arterial disease (PAD) is a prevalent and insidious disease caused by atherosclerosis, potentially leading to total occlusion of artery and gangrene of leg. The most common risk factors for this limb-threatening disease are type 2 diabetes mellitus, ageing, and cigarette smoking, but the pathogenesis of atherosclerosis may include hypertension, dyslipidemia, and homocysteinemia.
Underdiagnosis and under-treatment of PAD are partly because of its stealthy progress and lack of screening device for early diagnosis and active monitoring. Typical clinical manifestations of this vascular disorder are intermittent claudication and leg pain with unknown degree of arterial obstruction. In tertiary hospitals PAD can be accurately diagnosed with invasive angiography and ankle-brachial pressure index (ABI), currently deemed as a standard for evaluating severity. The severity is generally divided into normal (ABI 〉 0.9), low-grade (ABI = 0.9-0.5), and high-grade (ABI 〉 0.9) based on the ABI. Unfortunately, it is not sensitive enough to be used for prognostic evaluation of patients with hardened arteries commonly observed in diabetic and uremic.
Photoplethysmography (PPG) is an optic technique based on the association of blood volume change with light-tissue interaction. In current clinical setting, measurement of peripheral oxygenation and cardiac rhythm highly rely on this noninvasive technique. Previous studies have reported that the differences of pulse transit time (PTT) of photoplethysmograms between the right and left feet are significantly greater in PAD patients than those in healthy persons. However, a PPG-based assistant device for the diagnosis of PAD is still lacking.
The objective of this thesis is to develop a computer-assisted tool as an assistant tool for PAD diagnosis. The prototype was designed by combining dynamic error system of fractional-order chaos synchronization and pattern recognition techniques to test its potential in clinical applications. In the first experiment, photoplethysmographic signals were captured from 25 recruited subjects, including 11 healthy adults and 14 diabetic patients with three degrees of disease severity. Taking R wave of electrocardiogram as the reference, parameters △PTTp, △PTTf and △RT are determined from big toes of two feet. The results show that the dynamic errors of the fractional-order chaos synchronization and color relational analysis are able to effectively classify 3 different degrees of PAD severity. In the second experiment, 15 healthy persons and 17 diabetic patients were recruited for PPG measurement. The classification of PAD severity is also effectively conducted using support vector machine to design the classifier with wolf pack search algorithm adopted for obtaining optimal model parameters. Compared to the artificial neural network and other machine learning techniques, the proposed method is demonstrated to be efficient and effective to estimate the PAD severity.
Photoplethysmography combined with proper classification techniques consisting of color relational analysis and support vector machine is potential to design a portable computer-assisted tool for real-time PAD diagnosis. Its advantages include only small sample data are required for model training; patterns are expandable; signal capture and model training are efficient; parameter assignment is not necessary; and trapped in local minima can be avoided. Furthermore, electrocardiogram may be neglected for a PPG to be analyzed with dynamic error system of fractional-order chaos synchronization. In conclusion, PPG analyzed with color relation and modeled with support vector machine is potential in designing an assistant tool to screen and monitor the PAD in communities and hospitals.

ACKNOWLEDGMENTS I
CONTENTS II
LIST OF FIGURES IV
LIST OF TABLES V
ABBREVIATIONS VI
ABSTRACT VIII
中文摘要 X
CHAPTER 1 INTRODUCTION 1
1.1 topic of this research 8
1.2. The goals of this research 8
1.3. Engineering design and product development 8
1.4. Contributions of this research 9
CHAPTER 2 METHODOLOGY AND TECHNIQUE 11
2.1. Introduction to peripheral arterial disease 11
2.2. Photoplethysmography 13
2.2.1. Basic principles of photoplethysmography 14
2.2.2. History of photoplethysmography 15
2.2.3. Instrumentation of photoplethysmography 17
2.2.4. Analysis of photoplethysmographic waveform 18
2.2.5. Clinical applications of photoplethysmography 19
2.3. Pattern recognition 21
2.3.1. Introduction to pattern recognition 21
2.3.2. Support vector machine 23
2.3.3. Color relational analysis 26
2.4. Fractional order derivatives 32
2.4.1. Introduction to fractional order derivatives 32
2.4.2. Principle of fractional order calculus 33
2.4.3. Applications of fractional order calculus 35
2.5. Chaos synchronization 35
2.5.1. Introduction to chaos synchronization 36
2.5.2. Basic principle of chaos synchronization 37
2.5.3. Applications of chaos synchronization 38
CHAPTER 3 EXPERIMENT AND INSTRUMENTATION 40
3.1. Background 42
3.2. Objective 44
3.3. Design of experiments 44
3.3.1. Photoplethysmography instrumentation 44
3.3.2. Photoplethysmographic signals 45
3.3.3. Fractional-order chaos synchronization of PPG signals 46
3.3.4. Color relational analysis 53
3.3.5. Support vector machine implementation 56
3.3.6. Wolf Pack Search 58
CHAPTER 4 METHODS AND PATIENTS 62
CHAPTR 5 RESULTS 65
5.1 Fractional-order chaos synchronization and color relational analysis 65
5.2 Support vector machine and wolf pack search 70
5.3 Performance comparison 75
CHAPTER 6 DISCUSSION 80
6.1 Summary 81
6.2 Further perspective 82
6.3 Conclusion 83
BIBLIOGRAPHY 86

[1] F. J. SHernando, and A. M. Conejero, “Peripheral artery disease: pathophysiology, diagnosis and treatment, Rev Esp Cardiol, vol. 60, pp. 969-82, 2007.
[2] http://en.wikipedia.org/wiki/Atherosclerosis.
[3] B. A. Lipsky, A. R. Berendt, P. B. Cornia, J. C. Pile, E. J. G. Peters, D. G. Armstrong et al., “Infectious Diseases Society of America Clinical Practice Guideline for the Diagnosis and Treatment of Diabetic Foot Infections, Clin Infect Dis, vol. 54, pp. 132-73, 2012.
[4] http://www.cardiosource.org/~/media/Files/Science%20and%20Quality/Guidelines/ Pocket%20Gu.
[5] S. Ahn, Y. J. Park, S. I. Min, S. Y. Kim, J. Ha, S. J. Kim, et al., “High prevalence of peripheral arterial disease in Korean patients with coronary or cerebrovascular disease, J Korean Med Sci, vol. 27, pp. 625-629, 2012.
[6] P. C. Bennett, S. Silverman, P. S. Gill, and G. Y. H. Lip. “Ethnicity and peripheral artery disease, Q J Med, vol. 102, pp. 3-16, 2009.
[7]B. A. Golomb, T. T. Dang, and M. H. Criqui “Peripheral arterial disease
morbidity and mortality implications, Circulation, vol. 114, pp. 688-699, 2006.
[8]M. H. Criqui, “Peripheral arterial disease-epidemiological aspects. Vascular Medicine, vol. 6, pp. 3–7S, 2001.
[9]K. Wattanakita, A. R. Folsoma, E. Selvinb, B. D. Weatherleyc, J. S. Pankowa, F. L. Brancatib, et al. “Risk factors for peripheral arterial disease incidence in persons with diabetes, the Atherosclerosis Risk in Communities (ARIC) Study, Atherosclerosis, vol. 180, pp. 389-97, 2005.
[10]S. C. Smith, E. J. Benjamin, R. O. Bonow, L. T. Braun, M. A. Creager, B. A. Franklin, et al., “AHA/ACCF secondary prevention and risk reduction therapy for patients with coronary and other atherosclerotic vascular disease: 2011 update, Circulation, vol. 124, pp. 2458-73, 2011.
[11]http://www.ris.gov.tw/zh_TW/346.
[12]K. Cassar, “Peripheral arterial disease, Clin Evid, vol. 1, pp. 211-85, 2011.
[13]J. J. Mourad, P. Cacoub, J. P. Collet, F. Becker, J. F. Pinel, D. Huet, et al., “Screening of unrecognized peripheral arterial disease using ankle-brachial index in high cardiovascular risk patients free from symptomatic PAD, J Vasc Surg, vol. 50, pp. 572-80, 2009.
[14]A. Reisner, P. A. Shaltis, D. McCombie, and H. H. Asada, “Utility of the photoplethysmogram in circulatory monitoring Anesthesiol, vol. 108, pp. 950–8, 2008.
[15]M. Elgendi, “On the analysis of fingertip photoplethysmogram signals, Current Cardiol Rev, vol. 8, pp. 14-25, 2012.
[16]http://www.cs.tau.ac.il/~nin/Courses/Workshop12a/PPG%20Sensor%20System.pdf.
[17]J. Allen, “Photoplethysmography and its application in clinical physiological measurement, Physiol Meas, vol. 28, pp. 1–39, 2007.
[18]J. Allen, C. P. Oates, T. A. Lees, and A. Murray, “ Photoplethysmography detection of lower limb peripheral arterial occlusive disease: a comparison of pulse timing, amplitude and shape characteristics, Physiol Meas, vol. 26, pp. 811–21, 2005.
[19]J. Allen, K. Overbeck, A. F. Nath, A. Murray, and G. Stansby, “A prospective comparison of bilateral photoplethysmography versus the ankle-brachial pressure index for detecting and quantifying lower limb peripheral arterial disease, J Vasc Surg, vol. 47, pp. 794-802, 2008.
[20]N. Khandanpour, Y. K. Loke, F. J. Meyer, B. Jennings, and M. P. Armon, “ Homocysteine and peripheral arterial disease: Systematic review and meta-analysis, Eur J Vasc Endovasc Surg, vol. pp. 38, 316-22, 2009.
[21]http://www.cdc.gov/dhdsp/data_statistics/fact_sheets/fs_pad.htm.
[22]J. Li, B. Hasimu, J. Yu, J. Wang, and D. Hu, “Prevalence of peripheral arterial disease and risk factors for the low and high ankle-brachial index in Chinse patients with type 2 diabetes, J Health Sci, vol. 52, pp. 97-106, 2006.
[23]L. Uccioli, E. Pampana, R. Gandini, V. Spallone, L. Giurato, E. Vainieri, et al.,Long-term outcomes of diabetic patients with critical limb ischemia followed in a tertiary referral diabetic foot clinic, Diabetic care, vol. 33, pp. 33 977-82, 2010.
[24]C. White, “Intermittent claudication, N Eng J Med, vol. 356, pp. 1241-50, 2007.
[25]R. Collins, J. Burch, G. Cranny, R. Agular-Ibanez, D. Craig, K. Wright, et al., “Duplex ultrasonography, magnetic resonance angiography, and computed tomography angiography for diagnosis and assessment of symptomatic, lower limb peripheral arterial disease: systematic review, Br J Med, doi: 10.1136/bmj.39217.473275.55, pp. 1-9, 2007.
[26]N. A. Khan, S. A. Rahim, S. A. Anand, D. L. Simel, and A. Panju, “Does the clinical examination predict lower extremity peripheral arterial disease?, JAMA, vol. 295, pp. 536-46, 2006.
[27]D. Xu, J. Li, L. Zou, Y. Xu, D. Hu, S. L. Pagoto, and Y. Ma, “Sensitivity and specificity of the ankle-brachial index to diagnose peripheral artery disease: a structured review, Vasc Med. 15 361-369, 2010.
[28]S. P. A. Nicolai, L. M. Kruidenier, E. V. Rouwet, M. L. E. L. Bartelink, M. H. Prins, and J. A. W. Wijink, “Ankle brachial index measurement in primary care: are we doing it right?, Br J Gen Pract, vol. 59, pp. 422-7, 2009.
[29]T. H. Khan, F. A. Farooqui, and K. Niazi, “Critical review of the ankle brachial index, Curr Cardiol Rev, vol. 4, pp. 101-6, 2008.
[30]D. Fleischmann, R. L. Hallett, and G. D. Rubin, “CT angiography of peripheral arterial disease, J Vasc Interv Radiol, vol. 17, pp. 3-26, 2006.
[31]http://www.who.int;features/factiles/diabetes/en/index.html.
[32]S. Wild, R. Sicree, G. Rolic, H. King, and A. Green, “Global prevalence of diabetes: estimates for the year 2000 and projections for 2030, Diabetic Care, vol. 27, pp. 1047-53, 2004.
[33]ADA, “American Diabetes Association Standards of medical care in diabetes, Diabetes Care, vol. 35, pp.11-6S, 2012.
[34]P. K. Garg, K. Liu, L. Tian, J. M. Guralnik, L. Ferrucci, M. H. Criqui, et al., “Physical activity during daily life and functional decline in peripheral arterial disease, Circulation, vol. 119, pp. 251-60, 2009.
[35]S. Rhee, “Design and analysis of artifact-resistive finger photoplethysmographic sensors for vital sign monitoring, Ph.D. MIT, 2000.
[36]G. V. G. Baranoski, and A. Krishnaswamy, “An introduction to light interaction with human skin, RITA, vol. 11, pp. 33-62, 2004.
[37]G. S. H. Chan, A. Fazalbhoy, I. Birznieks, V. G. Macefield, P. M. Middleton, and N. H. Lovell, “Spontaneous fluctuations in the peripheral photoplethysmographic waveform: roles of arterial pressure and muscle sympathetic nerve activity, Am J Physiol Heart Circ Physiol, vol. 302, pp. 826–36, 2012.
[38]W. Verkruysse, L. O. Svaasand, and J. S. Nelson, “Remote plethysmographic imaging using ambient light, Optics Express, vol. 26, pp. 21434-45, 2008.
[39]A. P. Avolio, M. Butlin, and A. Walsh, “Arterial blood pressure measurement and pulse wave analysis—their role in enhancing cardiovascular assessment, Physiol Meas, vol. 31, pp. 1-47R, 2010.
[40]M. Zaheditochai, R. Jaafar, and E. Zahedi, “Non-invasive techniques for assessing the endothelial dysfunction: Ultrasound versus photoplethysmography, ICBME Proceedings, vol. 23, pp. 65–8 2009.
[41]P. J. Chowienczyk, R. P. Kelly, H. MacCallum, S. C. Millasseau, T. L. G. Andersson, R. G. Gosling, et al., “Anggard Photoplethysmographic assessment of pulse wave reflection, J Am College Cardiol, vol. 34, pp. 2007–14, 1999.
[42]H. Molitor and M. Kniazuk, “A new bloodless method for continuous recording of peripheral change, J Phar Expr Ther, vol. 27, pp. 5-16, 1936.
[43]A. V. J. Challoner, “Photoelectric plethysmography for estimating cutaneous blood flow, in Non-Invasive Physiol Measur. London: Academic pp 125–51, 1979.
[44]A. B. Hertzman, “Photoelectric plethysmography of the fingers and toes in man Proc Soc Exp Bip Med, vol. 37, pp. 529-42, 1937.
[45]A. B. Hertzman, and J. B. Killon, “Distinction between arterial, venous and flow components in photoelectric plethysmography in man, Am J Physiol, vol. 130, pp. 177-85, 1940.
[46]http://www.freescale.com/files/32bit/doc/app_note?AN4327.pdf.
[47]Y. Maeda, M. Sekine, and T. Tamura, “The advantages of wearable green reflected photoplethysmography, J Med Syst, vol. 35, pp. 829-34, 2011.
[48]S. M. Lopez-Silva, R. Giannetti, M. L. Dotor, J. P. Silveira, D. Golmayo, F. Miguel-Tobal, et al., “Heuristic algorithm for photoplethysmographic heart rate tracking during maximal exercise test, J Med Biol Eng, vol. 32, pp. 181-188, 2011.
[49]J. Allen, C. P. Oates, J. Henderson, J.Jago, T. A. Whittingham, J. Chamberlain, et al., “Comparison of lower limb arterial assessments using color-duplex ultrasound and ankle brachial pressure index measurements, Angiography, vol. 47, pp. 225-32, 1996.
[50]A. A. Kamshilin, S. Miridonov, V. Teplov, R. Saarenheimo R, and E. Nippolainen, “Photoplethysmographic imaging of high spatial resolution, Biomed Optics Exp, vol. 2, pp. 996-1006, 2011.
[51]W. Verkruysse, L. O. Svaasand, and J. S. Nelson, “Remote plethysmographic imaging using ambient light, Biomed Optics Exp, vol. 16, pp. 21434-45, 2008.
[52]The New International Webster’s Comprehensive Dictionary of the English Language, 1998 ed., s.v. “pattern.
[53]http://www.icoachmath.com/math_dictionary/pattern.html.
[54]S. P. Shinde, and V. P. Deshmukh, “Implementation of pattern recognition techniques and overview of its applications in various areas of artificial intelligence, Internat J Adv Eng Tech, vol. 1, pp. 127-37, 2011.
[55]S. Theodoridis, and K. Koutroumbas, 2009 Pattern recognition. Canada: Academic Press.
[56]J. Liu, J. Sun, and S. Wang, “Pattern recognition: An overview, Internat J Comput Sci Network Security, vol. 6, pp. 57-61, 2006.
[57]R. R. Sokal, “Classification: purposes, principles, progress, prospects, Science, vol. 185, pp. 1115-23, 1974.
[58]S. B. Kotsiantis, “Supervised machine learning: A review of classification techniques, Informatica, vol. 31, pp. 249-68, 2007.
[59]C. C. H. Tang, P. M. Middleton, A. V. Savkin, G. S. H. Chan, S. Bishop S, and N. H. Lovel, “Non-invasive classification of severe sepsis and systemic inflammatory response syndrome using a nonlinear support vector machine: a preliminary study, Physiol Meas, vol. 31, pp. 775–93, 2010.
[60]D. Salas-Gonzalez, J. M. Gorriz, J Ramırez, M. Lopez, I. Alvarez, F. Segovia, et al., “Computer-aided diagnosis of Alzheimer’s disease using support vector machines and classification trees, Phys Med Biol, vol. 55, pp. 2807–17, 2010.
[61]T. Zeng, and J. Liu, “Mixture classification model based on clinical markers for breast cancer prognosis, Artif Intell Med, vol. 48, pp. 129-37, 2010.
[62]J. Sun, L. Han, and Z. Zhao, “Gene- and evidence-based candidate gene selection for schizophrenia and gene feature analysis, Artif Intell Med, vol. 48, pp. 99-106, 2010.
[63]N. Cristianini, and, J. Shawe-Taylor, “An introduction to support vector machines and other kernel-based learning methods, Cambridge University press, 2012.
[64]T. Nugent, “Transmembrane protein structure prediction using machine learning, Doctorate thesis. University College London. p97, 2010.
[65]B. Chen, and M. Johnson, “Protein local 3D structure prediction by super granule support vector Machines (Super GSVM), BMC Bioimform, vol. 10, pp. 11-15S, 2009.
[66]P. Sjda, “Machine learning for detection and diagnosis of disease, Annu Rev Biomed Eng, vol. 8, pp. 1-29, 2006.
[67]W. Yu, T. Liu, R. Valdez, M. Gwinn, and M. T. Khoury. “Application of support vector machine modeling for prediction of common diseases: the case of diabetes and pre-diabetes, BMC Med Inform Decision Making, doi:10.1186/1472-6947-10-16, 2010.
[68]A. J. Framea, P. E. Undrill, M. J. J. Cree, J. A. Olson, K. C. McHardy, P. F. Sharp, et al, “comparison of computer based classification methods applied to the detection of microaneurysms in ophthalmic fluorescein angiograms, Comput Biol Med, vol. 28, pp. 225-38, 1998.
[69]M. E. Mavroforakis, H. V. Georgiou, N. Dimitropoulos, D. Cavouras, and S. Theodoridis, “Mammographic masses characterization based on localized texture and dataset fractal analysis using linear, neural and support vector machine classifiers, Artif Intell Med, vol. 37, pp. 145-62, 2006.
[70]C. J. C, Burges, “A tutorial on support vector machines for pattern recognition, Data Mining Knowledge Discovery, vol. 2, pp. 121-167, 1998.
[71]http://www.clopinet.com/SVM.applications.html.
[72]C. H. Lin, M. S. Kang, C. H. Huang, and C. L. Kuo, “Fractal patterns for power quality detection using color relational analysis based classifier, World Acad Sci Engin Techol, vol. 41, pp. 588-64, 2010.
[73]D. Julong, “Introduction to grey system theory, J Grey Sys, vol. 1, pp. 1-24, 1989.
[74]X. R. Tan, Y. G. Li, and M. Z. Chen, “Applications of gray relational analysis in gastroenterology, World J Gastroenterol, vol. 11, pp. 3457-60, 2005.
[75]C. H. Lin, “Assessment of bilateral photoplethysmography for lower limb peripheral vascular occlusive disease using color relation analysis classifier, Comput Methods Programs Biomed, vol. 103, pp. 121-31, 2011.
[76]C. H. Lin, “Classification enhancible grey relational analysis for cardiac arrhythmias discrimination, Med Biol Eng Comput, vol. 44, pp. 311-20, 2006.
[77]R. Herrmann. “Fractional calculus: An introduction for physicistsm, World Scientific, 2011.
[78]M. Dalir, and M. Bashour, “Applications of fractional calculus, Appl Math Sci, vol. 21, pp. 1021-32, 2010.
[79]S. A. David, J. L. Linares, and E. M. J. A. Pallone, “Fractional order calculus: historical apologia, basic concepts and some applications, Revista Brasileira de Ensino de Fisica, vol. 33, pp. 4032-8, 2011.
[80]J. M. Kimeu, “Fractional calculus: Definitions and applications, Master theses of Western Kentucky University, doi:10.1186/1472-6947-10-16, 2009.
[81]C. Li, D. Qian, and Y. Chen, “On Riemann-Liouville and Caputo derivatives, Discrete Dynamics Natural Society. doi:10.1155/2011/562494, 2011.
[82]M. Javidi1, and N. Nyamoradi, “Numerical behavior of a fractional order HIV/AIDS epidemic model, World J Model Simulation, vol. 9, pp. 139-49, 2013.
[83]A. Zeb, G. Zaman, S. Momani, and V. Suaterturk, “Solution of an SEIR epidemic model in fractional order VFAST, Trans Appl Math, vol. 1, pp. 1-8, 2013.
[84]A. A. M. Arafa, S. Z. Rida, and M. Khalil, “Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection, Nonlinear Biomed Phys, vol. 6, pp. 1-7, 2012.
[85]E. Ahmed, and H. A. El-Saka, “On fractional order models for Hepatitis C, Nonlinear Biomed Phys, vol. 4, pp. 1-3, 2010.
[86]A. M. A. El-Sayed, S. Z. Rida, and A. A. M. Arafa, “On the solutions of time-fractional bacterial chemotaxis in a diffusion gradient chamber, Internat J Nonlinear Sci, vol. 7, pp. 485-492, 2009.
[87] K. Krishnaveni, K. Kannan, and S. R. Balachandar, “Approximate analytical solution for fractional population growth model, Internat J Engineer Tech, vol. 5, pp. 2832-36, 2013.
[88]D. Rostamy, and M. Jabbari, “Solutions of predator-prey populations from fractional integral operator Lotka-Volterra equations, J Appl Environ Biol Sci, vol. 2, pp. 159-71, 2012.
[89]D. Verotta, “Fractional dynamics pharmacolinetics-pharmacodynamic models, J Pharmacokinetic Pharmacodyn, vol. 37, pp. 257-76, 2010.
[90]J. P. Higgins, “Nonlinear systems in medicine, Yale J Biol Med, vol. 75, pp. 247-60, 2002.
[91]R. Kautz, “Chaos: the science of predictable random motion, Oxford University Press, 2012.
[92]C. Arrieta, and J. Navarro, “Chaos in human behavior,The case of work motivation, Span J Psychol, vol. 13, pp. 244-56, 2010.
[93]X. Wu, G. Chen, and J. Cai, “Chaos synchronization of the master–slave generalized Lorenz systems via linear state error feedback control, Physica D Nonlin Phenom, vol. 229, pp. 52-80, 2007.
[94]S. Kodba, M. Perc, and M. Marhl, “Detecting chaos from a time series, Euro J Physics, vol. 26, pp. 205-15, 2005.
[95]P. Geiger, and C. Dellago, “Identifying rare chaotic and regular trajectories in Lyapunov weighted path sampling, Chem Physics, vol. 375, pp. 309-15, 2010.
[96]L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, “Fundamentals of synchronization in chaotic systems, concepts, and application, Chaos, vol. 7, pp. 520-43, 1997.
[97]S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems, Phys Reports, vol. 366, pp. 1-101, 2002.
[98]L. M. Pecora, and T. L. Carroll, “Synchronization in chaotic systems, Physical Rev Letters, vol. 64, pp. 821-4, 1990.
[99]H. K. Chen, “Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lu, Chaos Solitions Fractals, vol. 25, pp. 1049-56, 2005.
[100]Y. Li, and B. Li, “Chaos control and projective synchronization of a chaotic Chen-Lee system, Chin J Physics, vol. 47, pp. 261-70, 2009.
[101]B. R. Andrievskii, and A. L. Fradkov, “Control of chaos: Methods and applications. II. Applications, Automation Remote Control, vol. 65, pp. 505-33, 2004.
[102]O. I. Olusola, U. E. Vincent, A. N. Njah, and E. Ali, “Control and synchronization of chaos in biological systems via backsteping design, Internat J Nonlinear Sci, vol. 11, pp. 121-8, 2011.
[103]H. Nijmeijer, “Control of chaos and synchronization,. System Contr Letters, vol. 31, pp. 259-62, 1997.
[104]H. Gehring, “Pulse oximeter in a comparative test, Intens Care Med, vol. 32 , pp. 1287-9, 2006.
[105]N. A. Khan, S. A. Rahim, S. S. Anand, D. L. Simel, and A. Panju, “Does the clinical examination predict lower extremity peripheral arterial disease?, J Am Med Assoc, vol. 295, pp. 536–46, 2006.
[106]J. Allen, and A. Muray, “Comparison of three arterial pulse waveforms classification techniques, J Med Engin Tech, vol. 20, pp. 109-14, 1996.
[107]P. Shi, “Photoplethysmography in noninvasive cardiovascular assessment, Doctorate thesis. Loughborough University p64, 2009.
[108]L. M. Tama, J. H. Chen, H. K. Chen, and W. M. S. Tou, “Generation of hyperchaos from the Chen–Lee system via sinusoidal perturbation, Chaos Solitons Fractals, vol. 38, pp. 826–39, 2005.
[109]J. H. Chen, “Controlling chaos and chaotification in the Chen-Lee system by multiple time delays, Chaos Solitons Fractals, vol. 36, pp. 843–52, 2008.
[110]H. K. Chen, and C. I. Lee, “Anti-control of chaos in rigid body motion, Chaos Solitons Fractals, vol. 21, pp. 957–65, 2004.
[111]K. S. Killer, and B. Ross, “An Introduction to the Fractional Calculus and Fractional Differential Equations, New York: Wiley, 1993.
[112]L. Dorcak, J. Valsa, J. Terpak, and E. Gonzalez, “Comparison of the methods of the calculation of fractional-order differential equation, 12th IEEE Intern Carpathian Control Conference, pp 84-8, 2010.
[113]L. M. Tam, and, W. M. S. Tou, “Parametric study of the fractional-order Chen–Lee system, Chaos Solitons Fractals, vol. 37, pp. 817–26, 2008.
[114]J. E. Naschitz, S. Bezobchuk, R. Mussafia-Priselac, S. Sundick, D. Dreyfuss I. Khorshidi, et al., “Pulse transit time by R-wave-gated infrared photoplethysmography: review of the literature and personal experience, J Clin Monit Comput, vol. 18, pp. 333–42, 2004.
[115]J. Kamruzzaman, and R. K. Begg, “Support vector machines and other pattern recognition approaches to the diagnosis of cerebral palsy gait, IEEE Trans Biomed Engin, vol. 53, pp. 2479-90, 2006.
[116]Y. Peng, Y. Zhang, and L. Wang, “Artificial intelligence in biomedical engineering and informatics: An introduction and review, Artif Intell Med, vol. 48, pp. 71-3, 2010.
[117]J. A. Ruiz-Vanoye, O. Díaz-Parra, F. Cocón, A. Soto, M. D. A. B. Arias, G. Verduzco-Reyes, et al, “Meta-heuristics algorithms based on the grouping of animals by social behavior for the traveling salesman problem, Internat J Combinat Opti Probl Informatics, vol. 3, pp. 104-23, 2012.
[118]H. S. Chang, “Converging marriage in honeybees optimization and application to stochastic dynamic programming, J Global Optim, vol. 35, pp. 423-41, 2006.
[119]C. Yang, X. Tu, and J. Chen, “Algorithm of marriage in honeybees optimization based on the wolf pack search, Internat Conf Intell Perva Comput, Jeju Island, Korea, p462-7, 2007.
[120]Y. Celik, and E. Ulker, “A marriage in honey bee optimization approach to the asymmetric travelling salesman problem, Internat J Innov Comput Inform Contr , vol. 8, pp. 4123-32, 2012.
[121]http://arxiv.org/ftp/arxiv/papers/1112/1112.4133.pdf.
[122]J. E. Naschitz, S. Bezobchuk, R. Mussafia-Priselac, S. Sundick, D. Dreyfuss , I. Khorshidi, et al, “Pulse transit time by R-wave-gated infrared photoplethysmography: review of the literature and personal experience, J Clin Monit Comput, vol. 18, pp. 333-42, 2004.
[123]Y. C. Du, and C. H. Lin, “H Adaptive network-based fuzzy inference system for assessment of lower limb peripheral vascular occlusive disease, J Med Syst, vol. 36, pp. 301-10, 2012.
[124]H. T. Yau, C. L. Kuo, and J. J. Yan, “Fuzzy sliding mode control for a class of chaos synchronization with uncertainties, Internat J Nonlinear Sci Numer Simul, vol. 7, pp. 333-8, 2006.