Mathematics and statistics in anaesthesia:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
1998
|
| Series: | Oxford medical publications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 258 S. Ill., graph. Darst. |
| ISBN: | 0192623125 0192623133 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Part 1 Physiological and pharmacological modelling
1.1 Models and modelling
1.1.1 Introduction 4
1.1.2 The modelling process: physiological and statistical models 5
1.2 Inputs and outputs
1.2.1 The input output principle 6
1.2.2 CSF flow and intracranial pressure 7
1.2.3 CSF dynamics 8
1.3 Steady states: alveolar ventilation VA and Paco2
1.3.1 Modelling steady states: UA and Paco2 9
1.3.2 Modelling assumptions 10
1.3.3 Generalizing the model 11
1.3 A Surfaces and functions of two variables 12
1.4 Gas laws
1.4.1 The same equations, different model 13
1.5 Flux and the Fick principle
1.5.1 Flux and fluxoids 14
1.5.2 CO2 flux: Paco2 and VA 15
1.5.3 Cardiac output 0 by CO2 flux 16
1.5.4 0 by O2 uptake 17
1.6 Fick and cardiac output: dilution methods
1.6.1 Q by dye dilution 18
1.6.2 0 by thermodilution 20
1.7 Fick and cerebral blood flow
1.7.1 The Kety Schmidt method for cerebral blood flow (CBF) 22
X.I.2 The Kety Schmidt method and tissue capacitance 23
1.8 Apnoeic mass transfer oxygenation
1.8.1 Apnoeic oxygenation 24
1.8.2 FRC and distribution volume 25
1.8.3 Input and output in the FRC 26
1.8.4 Effects of pre oxygenation and 02 concentration 27
1.8.5 Apnoeic oxygenation and differential equations 28
MATHEMATICS AND STATISTICS IN ANAESTHESIA
2.10.4 Angular frequency 136
2.10.5 Sums of sinusoids 137
2.11 Functions of more than one variable
2.11.1 Surfaces 138
2.12 The derivative and differentiation
2.12.1 Modelling, gradients, and rates of change: the derivative 139
2.12.2 Limits 141
2.12.3 Differentiation 1 142
2.12.4 Differentiation 2 144 1
2.13 Maxima and minima |
2.13.1 Local behaviour of functions 145 t
2.14 Integrals
2.14.1 Anti differentiation: integration 147
2.14.2 Integration and areas under curves 149
2.14.3 Definite and indefinite integrals 150
2.14.4 Integration and areas: exponential models 151
2.15 Differential equations
2.15.1 Modelling with differential equations 152
2.15.2 First order equations 153
2.15.3 Second order equations 154
2.16 Numerical methods for differential equations
2.16.1 An approximate method of solution 155
Part 3 Probability and statistics
3.1 Probability models and simulation
3.1.1 Probability and statistical modelling 160
3.2 Simulating random events: anaphylactoid reactions to anaesthesia
3.2.1 The Poisson process 161
3.2.2 Counting events: the Poisson distribution 162
3.2.3 Poisson distribution: general features 1 163
3.2.4 Poisson distribution: general features 2 164
3.2.5 The cumulative Poisson distribution 165
3.2.6 Plausible and implausible outcomes 167
3.3 Waiting times in a Poisson process
3.3.1 The exponential distribution 168
3.4 Passing the fellowship examination
3.4.1 The binomial distribution 169
3.4.2 The binomial distribution: general features 170
3.4.3 Parameters, symmetry, and skewness 171
3.5 Measuring SVP: the normal distribution
3.5.1 Estimation and measurement error 172
3.6 Modelling with random variables
3.6.1 The uniform distribution 173
3.7 Sums and differences of random variables (RVs)
3.7.1 Adding RVs 174
3.7.2 The centralizing tendency 175 i
MATHEMATICS AND STATISTICS IN ANAESTHESIA i)
3.8 Probability
3.8.1 Rules of probability: conditional probability 177
3.9 Conditional probability and Bayes theorem
3.9.1 Predicting difficult intubation 178
3.9.2 Pre and post test probabilities 179
3.9.3 The test function 181
3.9.4 Specificity and sensitivity 182
3.10 Summary measures: location and dispersion
3.10.1 Location: the mean, the median, and the mode 183
3.10.2 Dispersion: total error functions 185
3.10.3 Summing deviations: the TEFfor the median 186
3.10.4 Summing squared deviations: the TEF of the mean 187
3.10.5 Total sum of squares, TSS: variance and standard deviation 188
3.11 The normal distribution
3.11.1 General features 189
3.11.2 The standard normal distribution 190
3.11.3 Transformations of the standard normal distribution 191
3.11.4 The cumulative standard normal distribution 193
3.12 Statistical inference
3.12.1 Population and sample 195
3.12.2 Estimation and decision making 196
3.13 Sample mean
3.13.1 SVP measurement again: estimation from the mean of a sample 197
3.13.2 SVP measurement: the sampling distribution of the mean 198
3.13.3 Estimation and confidence 200
3.14 Sample variance
3.14.1 Samples of unknown mean and variance 201
3.14.2 Sampling distribution 202
3.14.3 Expected value 203
3.14.4 The chi squared (x2) distribution 205
3.14.5 Adding squared deviations: more members of the chi squared (x2)
distribution 206
3.15 Significance testing
3.15.1 A simple test of significance 208
3.15.2 The sign test 210
3.15.3 General concepts 211
3.15.4 Errors 211
3.15.5 Test power 213
3.16 Samples of unknown mean and variance
3.16.1 The t distribution family 215
3.16.2 Inference on means of small samples: estimation and significance
testing 217
3.16.3 The paired t test: the Cl for a difference in means 219
3.16.4 Differences in means of independent samples: the two sample t test 221
3.16.5 Two sample t test 223
3.17 Categorical data
3.17.1 Cross classifications 226
3.17.2 Poisson processes again 228
3.17.3 The x2test for association 229
MATHEMATICS AND STATISTICS IN ANAESTHESIA j
3.18 Related variables: linear regression
3.18.1 Linear relationships between variables 231 j
3.18.2 Finding the line of best fit: least squares 233 •
3.18.3 Building blocks 234
3.18.4 Reducing the TSS 235
3.18.5 Completing the model and the RSS 236
3.18.6 Worked example 238
3.19 Related variables: correlation
3.19.1 The binormal distribution 240
3.19.2 The Pearson coefficient 242
3.19.3 Correlation and regression 244
3.19.4 The normal plot 246
3.20 Distribution free methods
3.20.1 The non parametric approach 247
3.120.2 The Mann Whitney test for difference in median 248
3.21 IOP revisited
3.21.1 Queues 250
Bibliography 251
Index 253
f
I
|
| any_adam_object | 1 |
| author | Cruickshank, Steven |
| author_facet | Cruickshank, Steven |
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| author_sort | Cruickshank, Steven |
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| callnumber-subject | RD - Surgery |
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| dewey-full | 617.9/6/0151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 617 - Surgery & related medical specialties |
| dewey-raw | 617.9/6/0151 |
| dewey-search | 617.9/6/0151 |
| dewey-sort | 3617.9 16 3151 |
| dewey-tens | 610 - Medicine and health |
| discipline | Medizin |
| format | Book |
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| spelling | Cruickshank, Steven Verfasser aut Mathematics and statistics in anaesthesia Steven Cruickshank Oxford [u.a.] Oxford Univ. Press 1998 X, 258 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford medical publications Anesthesie gtt Statistiek gtt Wiskunde gtt Mathematik Mathematisches Modell Statistik Anesthesia Anesthesia Mathematical models Anesthesia Mathematics Anesthesia Statistical methods Mathematics Models, Biological Pulmonary Gas Exchange Pulmonary gas exchange Mathematical models Statistik (DE-588)4056995-0 gnd rswk-swf Anästhesie (DE-588)4001833-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Lunge (DE-588)4036651-0 gnd rswk-swf Gasaustausch (DE-588)4136101-5 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Anästhesie (DE-588)4001833-7 s Mathematik (DE-588)4037944-9 s DE-604 Statistik (DE-588)4056995-0 s Lunge (DE-588)4036651-0 s Gasaustausch (DE-588)4136101-5 s Mathematisches Modell (DE-588)4114528-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008521553&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cruickshank, Steven Mathematics and statistics in anaesthesia Anesthesie gtt Statistiek gtt Wiskunde gtt Mathematik Mathematisches Modell Statistik Anesthesia Anesthesia Mathematical models Anesthesia Mathematics Anesthesia Statistical methods Mathematics Models, Biological Pulmonary Gas Exchange Pulmonary gas exchange Mathematical models Statistik (DE-588)4056995-0 gnd Anästhesie (DE-588)4001833-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Lunge (DE-588)4036651-0 gnd Gasaustausch (DE-588)4136101-5 gnd Mathematik (DE-588)4037944-9 gnd |
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| title | Mathematics and statistics in anaesthesia |
| title_auth | Mathematics and statistics in anaesthesia |
| title_exact_search | Mathematics and statistics in anaesthesia |
| title_full | Mathematics and statistics in anaesthesia Steven Cruickshank |
| title_fullStr | Mathematics and statistics in anaesthesia Steven Cruickshank |
| title_full_unstemmed | Mathematics and statistics in anaesthesia Steven Cruickshank |
| title_short | Mathematics and statistics in anaesthesia |
| title_sort | mathematics and statistics in anaesthesia |
| topic | Anesthesie gtt Statistiek gtt Wiskunde gtt Mathematik Mathematisches Modell Statistik Anesthesia Anesthesia Mathematical models Anesthesia Mathematics Anesthesia Statistical methods Mathematics Models, Biological Pulmonary Gas Exchange Pulmonary gas exchange Mathematical models Statistik (DE-588)4056995-0 gnd Anästhesie (DE-588)4001833-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Lunge (DE-588)4036651-0 gnd Gasaustausch (DE-588)4136101-5 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Anesthesie Statistiek Wiskunde Mathematik Mathematisches Modell Statistik Anesthesia Anesthesia Mathematical models Anesthesia Mathematics Anesthesia Statistical methods Mathematics Models, Biological Pulmonary Gas Exchange Pulmonary gas exchange Mathematical models Anästhesie Lunge Gasaustausch |
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