1   ALGORITHMS 

1. THE RECONSTRUCTION PROBLEM 
1.1. Why is EIT so hard? 3 
1.2. Mathematical setting 4 
1.3. Measurements and e1ectrodes 9 
1.4. Regularizing linear ill-posed prob1ems 10 
1.5. Regularizing EIT 19 
1.6. Total variation regularization 23 
1.7. Jacobian calculations 28 
1.8. Solving the forward problem: the finite element method 32
1.9. Measurement strategy 42 
1.10. Numerical examples 47 
1.11. Common pitfalls and best practice 50 
1.12. Further developments in reconstruction algorithms 52 
1.13. Practical applications 54 

2   HARDWARE

2. EIT INSTRUMENTATION
2.1. Introduction 67 
2.2. EIT system architecture 67 
2.3. Signal generation 69 
2.4. Voltage measurement 88 
2.5. Example EIT systems 95 
2.6. Discussion and conclusion 101 

3  APPLICATIONS

3. IMAGING OF THE THORAX BY EIT
3.1. General introduction 107 
3.2. Equipment 107 
3.3. Cardiac imaging 110 
3.4. Pu1monary perfusion measurements 113 
3.5. Assessment of regional lung function 117 
3.6. General summary and future perspectives 123 

4. EIT OF BRAIN FUNCTION
4.1. Introduction 127 
4.2. Physiological basis of EIT of brain function 129 
4.3. EIT systems developed for brain imaging 137 
4.4. EIT of slow evoked physiological activity in the brain 148 
4.5. EIT of epilepsy 154 
4.6. EIT in stroke 157 
4.7. EIT of neuronal depolarization 159 
4.8. Conclusion and future work 160 

5. BREAST CANCER SCREENING WITH EIT
5.1. Rationale for using impedance measurements for breast cancer screening 167 
5.2. Different approaches to breast EIT 171 
5.3. Clinical results summaries 173 

6. APPLICATIONS OF EIT IN THE GASTROINTESTINAL TRACT
6.1. Rationale for EIT within the gastrointestinal tract 186 
6.2. Methods of measurement of gastric emptying 188 
6.3. Ultrasonography 190 
6.4. EIT to measure gastric emptying 191 
6.5. Published data in support of EIT as a valid method to assess 
       gastric volume and residence time 194 
6.7. Paediatric studies 200 
6.8. Recent applications: use of EIT to measure gastric emptying during 
       continuous infusion of nasogastric feed 201 
6.9. Summary 201 
6.10. General conclusions 202 

7. OTHER CLINICAL APPLICATIONS OF EIT
7.1. Hyperthermia 207 
7.2. EIT imaging of intra-pelvic venous congestion 208 
7.3. Other possible applications 209 

4  NEW DIRECTIONS

8. MAGNETIC INDUCTION TOMOGRAPHY
8.1. Introduction 213 
8.2. The MIT signa1 214 
8.3. Coils and screening 215 
8.4. Signal demodulation 218 
8.5. Cancellation of the primary signa1 218 
8.6. Working imaging systems and proposed applications 220 
8.7. Image reconstruction 225 
8.8. Spatial resolution, conductivity resolution and noise 228 
8.9. Propagation delays 230 
8.10. Multi-frequency measurements 230 
8.11. Imaging permittivity and permeability 231 
8.12. Conclusions 232 

9. MAGNETIC RESONANCE EIT
9.1 Introduction 239 
9.2. Problem definition 242 
9.3. Forward problem and numerical techniques 244 
9.4. Measurement techniques in MREIT 256 
9.5. Image reconstruction algorithms 260 
9.6. MREIT images 274 
9.7. Possible applications of MREIT 288 
9.8. Current status and future of MREIT research 289 

10. ELECTRICAL TOMOGRAPHY FOR INDUSTRIAL APPLICATIONS
10.1. Introduction 295 
10.2. Data acquisition 298 
10.3. Data processing 307 
10.4. Industrial applications of electrical tomography 312 
10.5. Summary 338 

11. EIT: THE VIEW FROM SHEFFIELD
11.1. Beginnings 348 
11.2. Making images: applied potential tomography 349 
11.3. Differential imaging 352 
11.4. Collecting data 355
11.5. Multifrequency images 359 
11.6. The third dimension 363 
11.7. Clinical studies 364 
11.8. What we have learned 365 
11.9. The future of medical EIT 368 

12. EIT FOR MEDICAL APPLICATIONS AT OXFORD BROOKES 1985-2003

13. THE RENSSELAER EXPERIENCE
13.1. Early developments 388 
13.2. Reconstruction algorithms 391 
13.3. Hardware 395 
13.4. Applied currents 398 
13.5. Optimal currents 399 
13.6. Static in vivo images with non-circular boundary and optimal currents 400
13.7. 3D 400
13.8. In vivo applications 401 
13.9. Paying for it 403 
13.10. People 404 
13.11. Meetings 405 
13.12. Concluding remarks 406 

APPENDIXES

APPENDIX A. BRIEF INTRODUCTION TO BIOIMPEDANCE
A.l. Resistance and capacitance 411 
A.2. Impedance in biological tissue 416 
A.3. Other related measures of impedance 418 
A.4. Impedance measurement 420 
A.5. Relevance to EIT 421 

APPENDIX B. INTRODUCTION TO BIOMEDICAL EIT
B.l. Historical perspective 423 
B.2. EIT instrumentation 425 
B.3. EIT image reconstruction 435
B.4. Clinical applications 439 
B.5. Current developments 445