The 5th IEEE International Conference on E-Health and Bioengineering - EHB 2015
Grigore T. Popa University of Medicine and Pharmacy, Iaúi, Romania, November 19-21, 2015
978-1-4673-7545-0/15/$31.00 ©2015 IEEE
Developing Realistic 3D Numerical Conductivity
and Permittivity Phantom of the Human Forearm
from 10 Hz to 0.1 THz
Esuabom Dijemeni1+, Helena Lund-Palau1-, Cherry Nzekwu1-
Affiliation 1: Medical Technology Innovation Team, Medical Technology Developers,
London, United Kingdom, firstname.lastname@example.org
+: Corresponding technical author (primary); -: Corresponding medical author
Abstract– Understanding the conductivity and permittivity
properties of the human forearm has the potential of developing
classifiers to differentiate healthy bones from abnormal bones
suffering from osteoporosis or osteopaenia. The aim of the paper
is to present the segmentation of three T1 weighted MRI scans of
the human forearm for computational modelling of the
conductivity and permittivity properties from 10 Hz to 0.1 THz.
The 2D MRI scans are segmented into 18 different regions
according to anatomical composition. A linear interpolation was
applied to the 2D MRI images to produce a 3D image. Cole-Cole
equation was used to model the conductivity and permittivity
from 10 Hz to 0.1 THz. The result of the Cole-Cole equation was
applied to the 3D segmented images to produce a 3D
computational conductivity phantom and a 3D computational
permittivity phantom of the human forear m. Through this
successful study of the electromagnetic properties of the normal
healthy human forearm, there is the potential for the expansion
of the technique to enable early detection of unhealthy bone and
thus consider prompt treatment of the patients with this
Keywords– Osteoporosis; Conductivity; Permittivity;
Dielectric; Bone Disease.
The human bone is a biological material made up of mainly
calcium, magnesium and phosphorus . Bone resorption
occurs as a result of the activity of specialized bone cells
known as osteoclasts. These cells are responsible for breaking
down bone in order to increase the supply of calcium to the
blood stream . The destructive process is
counterbalanced by bone formation in order to maintain
normal bone mass.
Osteoporosis is a bone disease where bone resorption
occurs at a much faster rate compared to bone formation
. The result is micro-architectural deterioration of the
bone tissue, causing thinning and weakening of the skeletal
bones and overall low bone mass and low bone mineral
density. Osteoporosis often remains undetected until it is
complicated by bone fractures following minimal trauma.
Across the world, osteoporosis causes over 8.9 million
fractures each year, which equates to one fragility fracture
every 3 seconds . Yet such consequences can be prevented
if osteoporosis is detected early and treated promptly.
A bone affected by osteoporosis will have significantly
different electromagnetic properties compared to a healthy
bone, due to a reduction in conductivity and increase in
permittivity of the porous bone. However the first
fundamental step is to successfully model the dielectric
properties of normal bone, in order to provide a baseline for
the comparison of future abnormal findings.
The aim of this paper is to present a 3D conductivity
phantom and a 3D permittivity phantom of a healthy human
forearm using three T1 weighted MRI scans . The MRI
scans are in Fig. 1 below.
Figure 1. Three axial slice MRI scans of a normal human forearm:
position 1, position 2 and position 3 (Left to right; proximal to distal).
METHODS AND RESULTS
A. Edge Detection
To understand the boundaries which separate the different
regions, edge detection was applied to the image (MRI scan
at position 1) as used in the literature . The different
edge detection methods applied were: (i) Zero-Cross (ii)
Laplacian of Gaussian and (iii) Canny . These are shown
in Fig. 2.
Figure 2. Three methods of edge detection as applied to MRI scan at
position 1: Zero-cross, Laplacian of Gaussian, Canny (Left to right).
Upon review, the best edge detecting method is Canny edge
detection. The edges of the different regions in the forearm
were defined to an acceptable level.
B. Dielectric Mapping Data
Critical review showing five decades of measured dielectric
properties of biological tissues has been performed .
Three experimental techniques based on impedance analyzer
were developed based on the review . The experiment
swept a frequency network to measure the dielectric
properties of tissue in the frequency range of 10 Hz to 20
GHz. A parametric model, Cole-Cole equation, was applied
to define the dielectric properties of biological tissue as a
function of frequency .
A four-pole Cole-Cole equation used to model the dielectric
properties of biological tissue is :
where Ȧ is the angular frequency, ߝis the permittivity of
free space, İ(Ȧ) is the complex permittivity, n is the order of
the Cole–Cole model, ߝஶ is the high-frequency permittivity,
οߝ is the magnitude of the dispersion, ߬ is the relaxation
time constant, ן is the broadening of the dispersion, and ߪ
is the static ionic conductivity. The permittivity value is the
real part of ߝሺ߱ሻ and the conductivity value is the product of
the imaginary part of ߝሺ߱ሻ and ߝǤ
C. 3D Numerical Conductivity and Permittivity Phantom
I. IMAGE SEGMENTATION
The major challenge concerning the creation of the 3D
conductivity and permittivity phantoms was the segmentation
of the MRI scans.
Figure 3. Image histograms showing the intensities of various tissue types,
using MRI scan at position 1
The image histograms in Fig. 3 demonstrate that different
anatomical regions have similar, overlapping intensities;
while in other cases the same region has distinct intensity
values at different positions in the MRI scan (i.e. artery). In
order to overcome this difficulty the image segmentation
process was broken down into four steps: (1) detect the
region, (2) use image intensity to correct errors, (3) remodel
the corrected region and (4) combine the remodeled region
with previous detected region, until there are no more
detected regions. This process is depicted in Fig. 4.
Figure 4. Image Segmentation Process: (i) Detect (ii) Correct (iii)
Remodel (iv) Combine (Top left to bottom right).
The image was segmented into 18 different regions as
shown in Table 1.
TABLE I : Segmented Regions in the Bone
Regions Tissue component Media
Region 1 Cancellous bone of the radius 1
Region 2 Cancellous bone of the ulna 1
Region 3 Cortical bone of the ulna 2
Region 4 Cortical bone of the radius 2
Region 5 Pronator quadratus muscle 3
Region 6 Flexor digitorum profundus tendon,
flexor pollicis longus tendon, flexor
carpi ulnaris tendon, flexor digitorum
superficialis tendon, flexor carpi
Region 7 Ulnar artery 5
Region 8 Median nerve and ulnar nerve 6
Region 9 Flexor carpi ulnaris muscle 3
Region 10 Basilic vein 7
Region 11 Radial artery 5
Region 12 Extensor pollicis brevis tendon,
extensor carpi radialis longus tendon,
brachioradialis tendon, abductor
pollicis longus tendon
Region 13 Extensor digitorum tendon, extensor
Region 14 Extensor indicis muscle 3
Region 15 Extensor carpi ulnaris tendon 4
Region 16 Extensor carpi ulnaris muscle 3
Region 17 Fat 8
Region 18 Skin 9
The three 2D segmented MRI scans were then combined
together using linear interpolation to generate a 3D phantom,
producing a mesh with 0.1667 mm/cell resolution (Fig 5).
ݎ݁ݏ݈ݑݐ݅݊ ൌ ௪ௗ௧ ௧
where the width of the forearm is 50 mm and width of the
segmented image of the forearm is 300 cells. The resolution
of the image was reduced by applying a median, mode or
mean averaging filter.
Figure 5. 3D numberical Phantom: Combining the three 2D Segmented MRI
III. PERMITTIVITY AND CONDUCTIVITY DATA
The conductivity and permittivity were applied to the 3D
phantom to produce a 3D conductivity and permittivity
phantom, using the Cole-Cole equation (Fig. 6).
Figure 6. Result of Cole-Cole Equation: Permitivity (top) and Conductivity
Figure 7. 3D numerical permitivity and conductivity phantoms at x = 200,
y = 150, and z = 1. Permittivity (left) and conductivity (right).
Figure 8. 3D numerical permitivity and conductivity phantom at 2 GHz:
Permitttivity (top) and Conductivity (bottom).
Fig. 7 shows a representation of a slice of the 3D dielectric
phantom where z-axis = 1 is constant. Fig 8. shows a
representation of the slice of the 3D dielectric phantom where
x-axis = 250 cells is a constant.
The final program is summarized in Fig. 9 below:
Figure 9. Complete Program Algorithm: Detect, Correct. Remodel,
Combine, Interpolate, Model and Result.
Three axial MRI scans of a normal human forearm were
segmented by detecting each region and correcting the
detected region by applying an intensity window to remove
unwanted detected pixels, 18 different anatomical regions
were detected by using the image segmentation technique.
The three 2D segmented images were converted to a 3D
phantom by applying linear resolution interpolation. The
resolution of the mesh was 0.1667 mm/cell.
A four-pole Cole-Cole equation was used to model the
conductivity and permittivity properties of the forearm from
10 Hz to 0.1 THz. As frequency increased, the conductivity
of the bone increased and permittivity of the bone decreased.
The result of the four-pole Cole-Cole equation was applied to
the 3D phantom to produce a 3D conductivity and
permittivity phantom of a healthy human forearm.
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to create a fully
scans to form a
3D bone Phantom
scans to form a
3D bone Phantom
Filter the detected
region with an
Find the edge of
the region using
Fill the region
with the detected
Read the image
Convert image to
Correct the errors