APPENDIX C

Modelling the frequency dependence of the dielectric properties to a 4 dispersions spectrum.

INDEX

Guide to the Fitting Function

Summary of fitting parameters

 

The 4-Cole-Cole analysis was carried out on the following tissues:Graphic

  1. Aorta
  2. Bladder
  3. Blood
  4. Bone -Cancellous (contains red bone marrow)
  5. Bone -Cortical
  6. Bone -Marrow (infiltrated with blood)
  7. Bone -Marrow (not infiltrated)
  8. Breast fat
  9. Cartilage
  10. Cerebellum
  11. Cerebro Spinal Fluid
  12. Cervix
  13. Colon (lower and upper large intestine)
  14. Cornea
  15. Dura
  16. Eye (Sclera)
  17. Fat (mean value provided)
  18. Fat (not infiltrated)
  19. Gall Bladder
  20. Gall Bladder Bile
  21. Grey Matter
  22. Heart
  23. Kidney
  24. Lens Cortex
  25. Lens Nucleus (for lens use average of cortex and nucleus)
  26. Liver
  27. Lung -Deflated
  28. Lung -Inflated
  29. Muscle -Parallel (provided for comparison purposes)
  30. Muscle -Transverse (Radial field direction was along then across the fibre)
  31. Nerve (spinal chord)
  32. Ovary
  33. Skin -Dry
  34. Skin -Wet
  35. Small Intestine
  36. Spleen
  37. Stomach (also oesophagus, duodenum and all upper digestive track)
  38. Tendon
  39. Testis (prostate has a similar composition, expect similar dielectric properties)
  40. Thyroid (thymus has a similar water content, expect similar properties)
  41. Tongue
  42. Trachea
  43. Uterus
  44. Vitreous Humour
  45. White Matter

Fitting Function

The model selected for the dielectric data across the frequency range is a summation of 4-Cole-Cole expressions as reported in the text


This expression can be explicitly written in terms of the parameters as they are represented in the legend to the graphs (Equation corrected to avoid an error in the original document - D.Andreuccetti, IFAC-CNR)


is the permittivity of free space F/m and the angular frequency and

Summary Table

Tissue Type \ Parameter ef del1 tau1 (ps) alf1 del2 tau2 (ns) alf2 sig del3 tau3 (us) alf3 del4 tau4 (ms) alf4
Aorta 4.000 40.00 8.842 0.100 50 3.183 0.100 0.250 1.00E+5 159.155 0.200 1.00E+7 1.592 0.000
Bladder 2.500 16.00 8.842 0.100 400 159.155 0.100 0.200 1.00E+5 159.155 0.200 1.00E+7 15.915 0.000
Blood 4.000 56.00 8.377 0.100 5200 132.629 0.100 0.700 0.00E+0 159.155 0.200 0.00E+0 15.915 0.000
Bone (Cancellous) 2.500 18.00 13.263 0.220 300 79.577 0.250 0.070 2.00E+4 159.155 0.200 2.00E+7 15.915 0.000
Bone (Cortical) 2.500 10.00 13.263 0.200 180 79.577 0.200 0.020 5.00E+3 159.155 0.200 1.00E+5 15.915 0.000
Bone Marrow (Infiltrated) 2.500 9.00 14.469 0.200 80 15.915 0.100 0.100 1.00E+4 1591.549 0.100 2.00E+6 15.915 0.100
Bone Marrow (Not Infiltrated) 2.500 3.00 7.958 0.200 25 15.915 0.100 0.001 5.00E+3 1591.549 0.100 2.00E+6 15.915 0.100
Brain (Grey Matter) 4.000 45.00 7.958 0.100 400 15.915 0.150 0.020 2.00E+5 106.103 0.220 4.50E+7 5.305 0.000
Brain (White Matter) 4.000 32.00 7.958 0.100 100 7.958 0.100 0.020 4.00E+4 53.052 0.300 3.50E+7 7.958 0.020
Breast fat 2.500 3.00 17.680 0.100 15 63.660 0.100 0.010 5.00E+4 454.700 0.100 2.00E+7 13.260 0.000
Cartilage 4.000 38.00 13.263 0.150 2500 144.686 0.150 0.150 1.00E+5 318.310 0.100 4.00E+7 15.915 0.000
Cerebellum 4.000 40.00 7.958 0.100 700 15.915 0.150 0.040 2.00E+5 106.103 0.220 4.50E+7 5.305 0.000
Cerebro Spinal Fluid 4.000 65.00 7.958 0.100 40 1.592 0.000 2.000 0.00E+0 159.155 0.000 0.00E+0 15.915 0.000
Cervix 4.000 45.00 7.958 0.100 200 15.915 0.100 0.300 1.50E+5 106.103 0.180 4.00E+7 1.592 0.000
Colon 4.000 50.00 7.958 0.100 3000 159.155 0.200 0.010 1.00E+5 159.155 0.200 4.00E+7 1.592 0.000
Cornea 4.000 48.00 7.958 0.100 4000 159.155 0.050 0.400 1.00E+5 15.915 0.200 4.00E+7 15.915 0.000
Dura 4.000 40.00 7.958 0.150 200 7.958 0.100 0.500 1.00E+4 159.155 0.200 1.00E+6 15.915 0.000
Eye Tissues (Sclera) 4.000 50.00 7.958 0.100 4000 159.155 0.100 0.500 1.00E+5 159.155 0.200 5.00E+6 15.915 0.000
Fat (Average Infiltrated) 2.500 9.00 7.958 0.200 35 15.915 0.100 0.035 3.30E+4 159.155 0.050 1.00E+7 15.915 0.010
Fat (Not Infiltrated) 2.500 3.00 7.958 0.200 15 15.915 0.100 0.010 3.30E+4 159.155 0.050 1.00E+7 7.958 0.010
Gall Bladder 4.000 55.00 7.579 0.050 40 1.592 0.000 0.900 1.00E+3 159.155 0.200 1.00E+4 15.915 0.000
Gall Bladder Bile 4.000 66.00 7.579 0.050 50 1.592 0.000 1.400 0.00E+0 159.155 0.200 0.00E+0 15.915 0.200
Heart 4.000 50.00 7.958 0.100 1200 159.155 0.050 0.050 4.50E+5 72.343 0.220 2.50E+7 4.547 0.000
Kidney 4.000 47.00 7.958 0.100 3500 198.944 0.220 0.050 2.50E+5 79.577 0.220 3.00E+7 4.547 0.000
Lens Cortex 4.000 42.00 7.958 0.100 1500 79.577 0.100 0.300 2.00E+5 159.155 0.100 4.00E+7 15.915 0.000
Lens Nucleus 3.000 32.00 8.842 0.100 100 10.610 0.200 0.200 1.00E+3 15.915 0.200 5.00E+3 15.915 0.000
Liver 4.000 39.00 8.842 0.100 6000 530.516 0.200 0.020 5.00E+4 22.736 0.200 3.00E+7 15.915 0.050
Lung (Deflated) 4.000 45.00 7.958 0.100 1000 159.155 0.100 0.200 5.00E+5 159.155 0.200 1.00E+7 15.915 0.000
Lung (Inflated) 2.500 18.00 7.958 0.100 500 63.662 0.100 0.030 2.50E+5 159.155 0.200 4.00E+7 7.958 0.000
Muscle 4.000 50.00 7.234 0.100 7000 353.678 0.100 0.200 1.20E+6 318.310 0.100 2.50E+7 2.274 0.000
Nerve 4.000 26.00 7.958 0.100 500 106.103 0.150 0.006 7.00E+4 15.915 0.200 4.00E+7 15.915 0.000
Ovary 4.000 40.00 8.842 0.150 400 15.915 0.250 0.300 1.00E+5 159.155 0.270 4.00E+7 15.915 0.000
Skin (Dry) 4.000 32.00 7.234 0.000 1100 32.481 0.200 0.000 0.00E+0 159.155 0.200 0.00E+0 15.915 0.200
Skin (Wet) 4.000 39.00 7.958 0.100 280 79.577 0.000 0.000 3.00E+4 1.592 0.160 3.00E+4 1.592 0.200
Small Intestine 4.000 50.00 7.958 0.100 10000 159.155 0.100 0.500 5.00E+5 159.155 0.200 4.00E+7 15.915 0.000
Spleen 4.000 48.00 7.958 0.100 2500 63.662 0.150 0.030 2.00E+5 265.258 0.250 5.00E+7 6.366 0.000
Stomach 4.000 60.00 7.958 0.100 2000 79.577 0.100 0.500 1.00E+5 159.155 0.200 4.00E+7 15.915 0.000
Tendon 4.000 42.00 12.243 0.100 60 6.366 0.100 0.250 6.00E+4 318.310 0.220 2.00E+7 1.326 0.000
Testis 4.000 55.00 7.958 0.100 5000 159.155 0.100 0.400 1.00E+5 159.155 0.200 4.00E+7 15.915 0.000
Thyroid 4.000 55.00 7.958 0.100 2500 159.155 0.100 0.500 1.00E+5 159.155 0.200 4.00E+7 15.915 0.000
Tongue 4.000 50.00 7.958 0.100 4000 159.155 0.100 0.250 1.00E+5 159.155 0.200 4.00E+7 15.915 0.000
Trachea 2.500 38.00 7.958 0.100 400 63.662 0.100 0.300 5.00E+4 15.915 0.200 1.00E+6 15.915 0.000
Uterus 4.000 55.00 7.958 0.100 800 31.831 0.100 0.200 3.00E+5 159.155 0.200 3.50E+7 1.061 0.000
Vitreous Humor 4.000 65.00 7.234 0.000 30 159.155 0.100 1.500 0.00E+0 159.155 0.000 0.00E+0 15.915 0.000

Aorta fitting model



Bladder fitting model



Blood fitting model



Bone Cancellous fitting model



Bone Cortical fitting model



Bone Marrow (Infiltrated) fitting model



Bone Marrow (Not Infiltrated) fitting model



Breast Fat fitting model



Cartilage fitting model



Cerebellum fitting model



Cerebro Spinal Fluid fitting model



Cervix fitting model



Colon fitting model



Cornea fitting model



Dura fitting model



Eye (Sclera) fitting model



Fat (Infiltrated) fitting model



Fat (Not Infiltrated) fitting model



Gall Bladder fitting model



Gall Bladder Bile fitting model



Grey Matter fitting model



Heart fitting model



Kidney fitting model



Lens Cortex fitting model



Lens Nucleus fitting model



Liver fitting model



Lung Deflated fitting model



Lung Inflated fitting model



Muscle (parallel fibers) fitting model



Muscle (transverse fibers) fitting model



Nerve fitting model



Ovary fitting model



Skin (Dry) fitting model



Skin (Wet) fitting model



Small Intestine fitting model



Spleen fitting model



Stomach fitting model



Tendon fitting model



Testis fitting model



Thyroid fitting model



Tongue fitting model



Trachea fitting model



Uterus fitting model



Vitreous Humour fitting model



White Matter fitting model




Pages written by Sami Gabriel

Last updated 6 November 1997



Please send comments and suggestions to Sami Gabriel or Patrick Mason