njit-etd2003-081 - New Jersey Institute of Technology

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227 5.6 Principal Component Analysis As mentioned in section 3.14, the principal components were arranged in order of decreasing variance with the most informative principal component listed first, and the least informative listed last. The dimensionality of the problem was reduced, i.e., reduces the number of variables without losing much of the information. Thus instead of analyzing a large number of the original variables with complex interrelationships, the data could be analyzed by a small number of uncorrelated principal components. Figure 5.60 presented a principal component plot of the data set containing 48 COPD and 8 normal subjects at rest. The data set gave the following principal components (PC): 1 st PC: LF_coh_HR_rsp — Coherence of HR and respiration signals in the LF range (0.04 - 0.15 Hz). 2nd PC: HF _ coh _ BP _rsp — Coherence of BP and respiration signals in the HF range (0.15 - 0.4 Hz). 3 rd PC: rsp — The respiration rate. This indicated that the largest variance between COPD and normal subjects was the interrelationships between heart rate and respiration. The second largest variance was the interrelationships between blood pressure and respiration. The third largest variance was the respiration rate itself.
228 Figure 5.60 Normal and COPD classification using principal component analysis (PCA). Note: (o: Normal; +: COPD) Table 5.6 Principal Components from Normal and COPD Data P1 P2 P3 Categories 0.0351 -0.3625 0.3099 rsp 0.2960 -0.1943 0.0928 HR 0.2729 -0.2367 0.1637 BP 0.3800 0.0271 -0.0793 LF_coh HR_rsp 0.2725 -0.0886 -0.3849 LF_coh_HR_BP 0.3349 0.2178 -0.0244 LF coh BP rsp 0.3416 0.0691 -0.0556 HF_coh_HR_rsp 0.1389 0.1252 -0.5128 HF cohHRBP 0.1924 0.4961 0.0194 HF_coh BP rsp 0.3386 -0.2607 0.0482 LF_pcoh_HR_rsp 0.0449 0.0540 -0.0351 LFpcoh_HR_BP 0.3341 0.1433 0.0701 LFpcoh_BP rsp 0.2954 -0.2978 0.2039 HF_pcoh_HR_rsp -0.0170 -0.2281 -0.5558 HF_pcoh_HR_BP 0.1308 0.4691 0.2969 HF_pcoh_BP_rsp
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Copyright Warning & Restrictions Th
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ABSTRACT TIME-FREQUENCY INVESTIGATI
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TIME-FREQUENCY INVESTIGATION OF HEA
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APPROVAL PAGE TIME-FREQUENCY INVEST
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BIOGRAPHICAL SKETCH (Continued) D.A
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ACKNOWLEDGMENT The author wishes to
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TABLE OF CONTENTS Chapter Page 1 IN
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TABLE OF CONTENTS (Continued) Chapt
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LIST OF FIGURES Figure Page 2.1 The
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LIST OF FIGURES (Continued) Figure
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LIST OF FIGURES (Continued) Figure
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ABBREVIATIONS A ABP Arterial Blood
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ABBREVIATIONS (Continued) P PID Pro
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2 mortality and sudden death. [2] B
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4 1) Patients with severe pulmonary
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6 examined for determining the inte
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8 identified using principal compon
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1 0 1. Present the application of t
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12 1.3 Outline of the Dissertation
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CHAPTER 2 PHYSIOLOGY BACKGROUND Bio
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16 Figure 2.2 The systemic and pulm
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18 illustrated in Figure 2.3. The i
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20 2.2 Blood Pressure The force tha
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22 2.4 The Nervous System Human beh
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24 The sympathetic nerve fibers lea
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26 Without these sympathetic and pa
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28 center in the medulla, which con
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30 Figure 2.6 Autonomic innervation
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32 average heart rate was measured
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34 However, they do note that there
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Figure 2.9 The placement of the pos
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38 female. While more men suffer fr
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40 Stage II: Moderate COPD - Worsen
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CHAPTER 3 ENGINEERING BACKGROUND Th
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44 Two common types of time-frequen
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46 STFT: Short-Time Fourier Transfo
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48 3.3 The Analytic Signal and Inst
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50 The advantage of using equation
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52 3.5 Covariance and Invariance Th
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where H(f), S(f) are Fourier transf
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56 Another shortcoming of the spect
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58 should take the kernel of the WD
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60 called the cross Wigner distribu
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62 3.6.3 The Choi-Williams (Exponen
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64 Figure 3.3 Performance of the Ch
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66 [-Ω,Ω ], then its STFT will be
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68 This condition forces that the w
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70 where c is a constant. Thus, the
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Figure 3.5 The time-frequency plane
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74 The measure dadb used in the tra
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76 and the wavelet transform repres
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78 Figure 3.6 Figure depicting the
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80 The final step to obtain the pow
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82 It should be noted that if the w
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84 The normal respiration rate can
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Figure 3.12 Power spectrum of BP II
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RR similar manner to give: When com
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90 when there is significant correl
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92 3.12 Partial Coherence Analysis
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94 after removal of the effects of
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96 The bulk of the theory and appli
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98 technique is measurement time. T
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100 usually attainable. The key poi
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102 variability exists in the propa
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104 eXogenous input (ARX) was used
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106 The baroreflex, an autonomic re
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108 the principal components are no
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110 The mathematical solution for t
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112 3.15 Cluster Analysis The term
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114 formed) one can read off the cr
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116 3.15.5 Squared Euclidian Distan
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118 Alternatively, one may use the
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120 Sneath and Sokal used the abbre
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122 may seem a bit confusing at fir
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CHAPTER 4 METHODS The purpose of th
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126 4.1.2.1 Autonomic Testing. HR V
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128 of heart rate, blood pressure,
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130 The patients who underwent LVRS
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132 panel of the Correct.vi. It was
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134 4.2.3 Power Spectrum Analysis o
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136 weighted-average value of the c
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138 For each given scale a within t
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140 frequency F to the wavelet func
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142 4.2.8 System Identification Ana
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144 In this study a simpler approac
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146 Table 4.2 Parameters That Make
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148 4.2.11 Cluster Analysis The sam
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150 viewing the time series of sequ
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Figure 5.2 BPV analysis of a COPD s
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Figure 5.3 HRV analysis of a normal
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Figure 5.4.1 Comparison of the HRV
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158 5.2 Time Frequency Analysis One
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Figure 5.5 Test signal with 3 sine
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162 Figure 5.6 (c) CWD of a signal
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164 Figure 5.7 (c) WT (dB4 wavelet)
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166 HRV more information about HRV
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168 Figure 5.9 (c) CWD plots of a n
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Figure 5.10 CWT (Morlet) HRV plot o
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172 The following figures show the
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174 Figure 5.15 CWT (Mexican Hat) H
Page 205 and 206: 176 5.2.5 Best Wavelet Selection fo
Page 207 and 208: 178 Table 5.1 Correlation Indices o
Page 209 and 210: 180 5.2.6 Vagal Tone and Sympathova
Page 211 and 212: 182 These figures basically show th
Page 213 and 214: 184 Figure 5.20 Sympathetic and par
Page 217 and 218: 188 5.2.7 Time-Frequency Analysis (
Page 219 and 220: 190 Figure 5.29 3D and contour plot
Page 221 and 222: 192 Figure 5.33 3D and contour plot
Page 229 and 230: Figure 5.44 Plot of raw respiration
Page 231 and 232: Figure 5.46 The LF partial coherenc
Page 233 and 234: Figure 5.48 HF partial coherence pl
Page 235 and 236: Table 5.2 Cross-Spectral Analysis o
Page 237 and 238: Table 5.3 Cross-Spectral Analysis o
Page 239 and 240: Figure 5.50 HF coherence of COPD (1
Page 241 and 242: 212 For better presentation of the
Page 243 and 244: Figure 5.53 Coherence and partial c
Page 245 and 246: 216 2. Interpretation of the transf
Page 247 and 248: 218 covariances of the parameters,
Page 249 and 250: 220 deviations are interpreted as A
Page 251 and 252: 222 Figure 5.58 Bode plot of the HR
Page 253 and 254: 224 In this section a simple model
Page 255: 226 The data for all 47 COPD subjec
Page 259 and 260: 230 Figure 5.61 Normal and COPD cla
Page 261 and 262: 232 Figure 5.62 Normal classificati
Page 263 and 264: 234 5.7 Cluster Analysis The purpos
Page 265 and 266: 236 Figure 5.64 Severity classifica
Page 267 and 268: 238 both the normal and COPD subjec
Page 269 and 270: 240 In summary, COPD subjects had h
Page 271 and 272: APPENDIX A EXERCISE PHYSIOLOGY A.1
Page 273 and 274: 244 A.3 Figure Out Your Target Hear
Page 275 and 276: APPENDIX B ANALYSIS PROGRAM LISTING
Page 277 and 278: 248 4) Click on file, close to exit
Page 279 and 280: 250 • TN 11
Page 281 and 282: 252 B.1.2 Partial Coherence Between
Page 283 and 284: 254
Page 285 and 286: 256 Block Diagram !rime of record K
Page 287 and 288: 258
Page 289 and 290: 260 B.2.2 Time — Frequency Analys
Page 291 and 292: 262 This program provides the STFT
Page 293 and 294: 264 G(:j+1)=G(:,j+1)/(2*sum(G(:j+1)
Page 295 and 296: 266 T=(length(Signa)/sample)/(Times
Page 297 and 298: 268 subplot(3, 1,3), plot(T,E); xla
Page 299 and 300: 270 4. The program creates five out
Page 301 and 302: 272 B.2.3.4 Program to Generate Sym
Page 303 and 304: 274 ylabel('frequency'); title('Ins
Page 305 and 306: 276 The program will run and output
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278 axis([0 1 0 2]); grid on; xlabe
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280 vagal=sum(TFDs(HFC,1:k)); symto
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282 plot(J,symtopar); %plot(A,symto
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284 4. Remove the constant levels a
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286 Make sure the agreement is quit
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288 B.2.6 Principal Components Anal
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290 Columns 12 through 15 'LF_pcoh_
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292 I= 1.0000 -0.0000 -0.0000 -0.00
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294 variances = 3.4083 1.2140 1.141
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296 B.2.7 Cluster Analysis Program
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298 end [R,C]=size(Data); if length
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300 B.2.8 Cross-correlation Program
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302 C.3 Partial coherence of HR and
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304 [13] Madwed, J., and R. Cohen.
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306 [41] Mallat, S. G., "A Theory f
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[70] Tazebay, M.V., R.T. Saliba and
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