Using Self Organizing Maps to Visualize Age Related Changes
in Lumbar Vertebrae and Intervertebral Discs
Atif Ali Khan*¹, Daciana Iliescu¹, Evor Hines¹, Charles Hutchinson², Robert Sneath³
¹School of Engineering, University of Warwick, ²Warwick Medical School, University of Warwick
³University Hospital Coventry and Warwickshire, NHS Trust, Coventry, United Kingdom
{Atif.Khan; E.L.Hines; D.D.Iliescu; C.E.Hutchinson}@warwick.ac.uk, robert.sneath@uhcw.nhs.uk
Abstract clinic, outnumbered only by the upper-respiratory
A human spine is a complicated structure of bones, joints, infections [1, 2, 3]. Back pain is one of the most common
ligaments and muscles which all undergo a process of reasons for missed work too. One-half of all working
change with age. This paper describes the use of artificial Americans admit to having back pain symptoms each year
intelligence in visualization and better understanding of the [1, 4]. Before finding the specific cause of back pain, it is
progressive and degenerative changes in human lumbar important to study the variation of spinal features with age
spine. Visualizing this pattern of change will be helpful in first and their correlation with one another [5]. These
finding the correlations among the spinal features and variations and correlation among the features were studies
understanding of how a change in one feature affects using the data collected from University Hospital Coventry
others. The self-organizing map (SOM) is an efficient tool and Warwickshire, United Kingdom in the form of
for visualization of multidimensional numerical data. It is magnetic resonance images (MRI) of the lumbar spine.
capable of projecting high-dimensional data onto a regular, Scoring of features (feature selection and extraction) was
usually 2-dimensional grid of neurons. In this paper, SOM done under the expertise of an orthopedic surgeon and
is used to visualize the pattern of change in lumbar spine radiologist. The model was designed and built using self-
features with the varying age. The paper gives an idea of
organizing maps.
how the information can be acquired from SOM
representations and how the SOM can be best utilized in
exploratory data visualization. Data from the lumbar spine A self-organizing map (SOM) is a special type of artificial
MRIs of 61 patients (both male and female) were used in neural network which is trained using unsupervised
this study. The age of patients ranged from 2 to 93 years. learning to produce a low-dimensional (typically two-
Information for vertebral height, disc height and disc signal dimensional), discretized representation of the input space
intensities were recorded from the MRI scans. SOM then of the training samples, called a map. Unlike to other
transformed the larger feature space to a smaller one for artificial neural networks, self-organizing map uses a
getting a more meaningful relation between the spinal neighborhood function to preserve the topological
features. Complexity is reduced and the data set is properties of the input space [6]. One of the most
represented in the form of 2D map which is easier to interesting aspects of SOMs is that they learn to classify
understand and provides visual description. data without supervision. With this approach an input
vector is presented to the network (typically a multilayer
I. Introduction feedforward network) and the output is compared with the
target vector. If they differ, the weights of the network are
A human spine is a complicated and key component of altered slightly to reduce the error in the output. This is
human being. During the normal ageing process, spine repeated many times and with many sets of vector pairs
undergoes progressive and regressive changes which until the network gives the desired output. Training a SOM
presumably follow certain pattern. This research focuses requires no target vector and learns to classify the training
explicitly on the study of progressive and degenerative data without any external supervision whatsoever [7]. To
changes occurring in the human lumbar spine with the study the variations and correlation of the spinal features, a
normal ageing process. This research work concentrates on model was built which assigns patient a certain cluster to
the identification and classification of age-related which he/she resembles the most on the basis of his/her
variations in "human spine" with the help of Magnetic spinal scores. This will help spine specialists to rank and
Resonance Image (MRI). These scans of the lumbar spine categorize patients on the basis of their spinal scores. This
area belong to patients of different age groups. Back pain research work will provide a better overview to the spine
is usually associated with the spine disorder. It is the specialists and the patients about the abnormal behavior if
second most common reason for visits to the doctor’s any shown by their spine.
II. Lumbar Spine MRI scans of 61 patients were selected to develop an initial
model. Age and gender distribution of patients are shown
A human spine consists of bones, joints, ligaments and in the Table 1 below. Ten groups were formed on the basis
muscles. There are a total of 33 vertebrae in the human of age decades as: G0: up to 10 years, G1: 11-20 years, G2:
spine: 7 in the neck (cervical region), 12 in the middle 21-30, years, G3: 31-40 years, G4: 41-50 years, G5: 51-60
back (thoracic region), 5 in the lower back (lumbar years, G6: 61-70 years, G7: 71-80 years, G8: 81-90 years
region), 5 that are fused to form the sacrum and the 4 and G9: 91 and above years of age).
coccygeal bones that form the tailbone [8]. The anatomy of
Table I. Age wise clustering of the samples
human spine is shown in the figure 1 below. The focus of
this research work is to look at the age related changes in Age Group Age (years) Female Male Total
the lumbar spine area. This lumbar spine area consists of Group 0 10 and younger 3 1 4
vertebrae L1, L2, L3, L4, L5 and intervertebral discs Group 1 11 to 20 2 4 6
between these vertebrae.
Group 2 21 to 30 4 2 6
Group 3 31 to 40 3 3 6
Group 4 41 to 50 3 2 5
Group 5 51 to 60 4 2 6
Group 6 61 to 70 6 2 8
Group 7 71 to 80 4 4 8
Group 8 81 to 90 4 3 7
Group 9 91 and over 2 3 5
Total 35 25 61
There are lots of notable features which can be studied
from a lumbar spine MRI scan. The scoring criteria were
set to look initially on the vertebral height (L1, L2, L3, L4
and L5), disc height (T12-L1, L1-L2, L2-L3, L3-L4, L4-L5
and L5-S1) and disc signal (T12-L1, L1-L2, L2-L3, L3-L4,
L4-L5 and L5-S1). These 17 spinal features were used as
Figure 1: Anatomy of human spine an input to build and test the initial model. These features
were measured and recorded from the lumbar spine MRIs
III. Data Set of 61 patients.
Table II. Extracted features of 5 samples from lumbar spine MRIs
The data set used in this research was taken from the
University Hospital Coventry and Warwickshire (UHCW), 1 2 3 4 5
United Kingdom. The raw data is in the form of Magnetic Gender m/f f f m m f
Resonance Images (MRI) specifically of the lumbar spine Age Years 8 23 40 68 89
area. The format of data is Digital Imaging and L1 16.94 22.82 27.16 23.95 21.7
Communications in Medicine (DICOM). These magnetic L2 17.34 22.98 27.16 23.57 22.06
resonance images are the actual scans of the patients. Vertebral height 16.8 24.57 26.08 23.53
L3 21.94
Figure 2, shows the lumbar spine MRI.
L4 17.34 24.65 27.85 23.53 21.33
L5 17.22 25.94 27.25 23.95 19.11
T12 L1 5.95 7.51 9.33 9.48 4.45
L1 L2 7.43 9.92 11.41 12.13 6.3
L2 L3 7.75 10.22 13.05 13.27 5.35
Disc height
L3 L4 8.34 10.84 12.67 15.15 4.69
L4 L5 8.0 9.06 11.83 15.41 7.15
L5 S1 6.84 11.13 7.71 10.74 5.35
T12 L1 272.4 132.5 189.4 138.8 61.9
L1 L2 268.6 126.1 180.8 127.9 69.6
L2 L3 255.1 123 185.2 120.2 43
Fig 2: Sagittal and an axial view of the lumbar spine MRI Disc Signal
L3 L4 307.6 104.4 208.7 129.9 75.1
263 95.3 138.4 137.6
Information associated with each MRI scan is the age and L4 L5 67.2
gender of the patient which is used for SOM modeling. L5 S1 260 109.3 52.6 57.4 89.6
IV. Methodology adapt their future responses to that input accordingly in
such a way that neurons of competitive networks physically
Self-organizing maps (SOMs) are a data visualization near each other in the neuron layer respond to similar input
technique invented by Teuvo Kohonen which reduces the vectors.
dimensions of data through the use of self-organizing
neural networks. As the humans simply cannot visualize
high dimensional data so this technique was created to help
us understand high dimensional data. The way SOMs go
about reducing dimensions is by producing a map of
usually 1 or 2 dimensions which plot the similarities of the
data by grouping similar data items together. So SOMs
accomplish two things, they reduce dimensions and
display similarities. The proposed model has a set of 17
input vectors arranged as columns in a matrix. SOM
groups or ranks each sample (patient) on the basis of
similarities in their 17 features and assigns certain location
to each sample in the map. Figure 3 below; shows the step Figure 4, Structure of self-organizing map
by step demonstration of the methodology used.
With SOM, clustering is performed by having several units
compete for the current object. Once the data have been
entered into the system, the network of artificial neurons is
trained by providing information about inputs. The weight
vector of the unit is closest to the current object becomes
the winning or active unit. During the training stage, the
values for the input variables are gradually adjusted in an
attempt to preserve neighborhood relationships that exist
within the input data set. As it gets closer to the input
object, the weights of the winning unit are adjusted as well
as its neighbors [12, 13]. SOM training is shown below:
Figure 3. Steps involved in modeling
V. Self-Organizing Maps
Self-Organizing Map (SOM) is a data visualization
technique which helps to understand high dimensional data
by reducing data dimensions and displaying similarities
among data. According to Teuvo Kohonen; the self- Figure 5. SOM training
organizing map (SOM) is a new, effective software tool
for the visualization of high dimensional data. It converts The self-organization process involves four major
complex, nonlinear statistical relationships between high- components:
dimensional data items into simple geometric relationships
on a low-dimensional display. As it thereby compresses Initialization: All the connection weights are initialized
information while preserving the most important with small random values.
topological and metric relationships of the primary data Competition: For each input pattern, the neurons compute
items on the display, it may also be thought to produce their respective values of a discriminant function which
some kind of abstractions [9]. provides the basis for competition. The particular neuron
with the smallest value of the discriminant function is
SOM contains two processes: training and mapping. In declared the winner.
training process, it constructs the map using input samples. Cooperation: The winning neuron determines the spatial
After the training, it automatically classifiers a new input location of a topological neighbourhood of excited neurons,
sample in the mapping process. The map consists of thereby providing the basis for cooperation among
several neurons which associated with a weight vector that neighbouring neurons.
has the same dimension as the input sample and a position Adaptation: The excited neurons decrease their individual
in the map. The neurons are arranged originally in physical values of the discriminant function in relation to the input
positions according to a topology function, such as a grid, pattern through suitable adjustment of the associated
hexagonal, or random topology. The purpose of SOM is to connection weights, such that the response of the winning
detect regularities and correlations in their input, and also neuron to the subsequent application of a similar input
to recognize groups of similar input vectors [10, 11]. It can pattern is enhanced.
SOM Algorithm: corresponding weight vector W, of n dimensions: (w1, w2,
w3...wn).
Unlike other learning technique in neural networks,
training a SOM requires no target vector. A SOM learns to VI. Experimentation
classify the training data without any external supervision.
Each node's weights are initialized. If the input space is D The measurements taken from the lumbar MRI of 61
dimensional (i.e. there are D input units) we can write the patients were used to model the SOM. Each patient has 17
input patterns as: features which were used as input to the model. These 17
input variables are vertebral heights (5 variables), disc
x = {xi: i = 1, …, D} height (6 variables) and disc signal (6 variables). So the
variables 1-5 are the vertebral height (L1-L5), variables 6-
And the connection weights between the input units i and 11 are the disc heights from T12/L1--L5/S1 and variables
the neurons j in the computation layer can be written as: 12-17 are the disc signals from T12/L1—L5/S1
respectively. The inputs vertebral heights, disc heights and
wj = {wji : j = 1, …, N; i = 1, …, D} disc signals have difference ranges. Initial model was built
without normalization of the inputs. Figure 7, below shows
“N” is the total number of neurons. To determine the best the SOM model built on the basis of 17 input variables
matching unit, one method is to iterate through all the without normalization. In this mode, final quantization
nodes and calculate the Euclidean distance between each error was: 47.292 and final topographic error was: 0.00.
node's weight vector and the current input vector. The
node with a weight vector closest to the input vector is
tagged as the BMU. The Euclidean distance is given as: U-matrix Variable1 Variable2 Variable3 Variable4
145 25.6 25.9 26.2 25.8
77 22.2 22.6 22.8 22.6
9.36 18.8 19.3 19.5 19.5
d d d d
Variable5 Variable6 Variable7 Variable8 Variable9
Where x is the current input vector and w is the node's 25.1 9.1 10.2 11.1 11.6
weight vector. 21.9 7.84 8.89 9.59 10.1
18.7 6.57 7.56 8.1 8.57
d d d d d
Network Architecture
Variable10 Variable11 Variable12 Variable13 Variable14
10.8 10.4 309 310 313
In SOM, the network is created from a 2D lattice of 9.03 8.94 179 178 180
'nodes', each of which is fully connected to the input layer. 7.28 7.43 49.1 46.5 46.1
Figure 6 shows a very small Kohonen network of 3 x 3 d d d d d
nodes connected to the input layer shown in dark blue. Variable15 Variable16 Variable17
332 333 299
188 188 170
43.6 42.9 40.3
d
SOM 24-Feb-2013 d d
Figure 7, 17 variables SOM without normalization of Inputs
Figure 6, SOM network architecture
Each node has a specific topological position (an x, y
coordinate in the lattice) and contains a vector of weights
of the same dimension as the input vectors. That is to say,
if the training data consists of vectors, X, of n dimensions:
(x1, x2, x3...xn). Then each node will contain a Figure 8, SOM and U-matrix without normalization of inputs
There are two separate parts of the SOM display. These U-matrix
3.16
Variable1
0.714
Variable2
0.709
Variable3
0.763
Variable4
0.766
include the unified matrix or U-matrix, and the component 1.79 -0.629 -0.713 -0.675 -0.684
planes that are provided for individual variables [14, 15]. 0.42
d
-1.97
d
-2.13
d
-2.11
d
-2.13
The U-matrix allows examination of the overall cluster Variable5
0.705
Variable6
0.683
Variable7
0.898
Variable8
1.14
Variable9
1.21
patterns in the input data set after the model has been
trained. [16, 17, 18] Each hexagonal cell represents -0.707 -0.349 -0.241 -0.149 0.00659
individual neurons, which are the mathematical linkages d
-2.12
d
-1.38
d
-1.38
d
-1.44
d
-1.2
between the input and output layers. Variable10
1.07
Variable11
1.13
Variable12
1.65
Variable13
1.73
Variable14
2
-0.0553 0.0264 0.395 0.461 0.617
The neurons are drawn into distinct clusters during model -1.18 -1.08 -0.856 -0.811 -0.762
training. Relative distances between neuron clusters are Variable15
d
Variable16
d
Variable17
d d d
displayed by the intensity of the colors, with dark color
2.04 1.86 1.75
representing greater distance [19, 20]. In the U-matrix 0.676 0.597 0.513
generated here, a strong cluster is apparent, occurring in d
-0.687
d
-0.67
d
-0.728
the top half (dark blue) and another one in the middle and SOM 23-Feb-2013
lower middle half (light blue). This indicates that most of Figure 10, SOM and U-matrix with normalized inputs
the input variables are covarying in one direction in n-
dimensional space (where n is the number of input
variables). A different trend is seen when SOM is modeled
VII. Results
with normalized data. When the input variables are In the component planes for individual variables, the color
normalized, following trend was seen as shown in figure 9 coding corresponds to actual numerical values for the input
below. variables that are referenced in the scale bars adjacent to
each plot. Blue colors show low values and red corresponds
to high values. The relationships between each of the
variables are visualized by comparing the color patterns for
individual maps. In this manner, the relationships between
all of the variables entered into the model can be examined
simultaneously or in pair-wise combinations.
U-matrix Variable1 Variable2 Variable3 Variable4
3.16 8.47 9.14 9.05 9.15
1.79 7.13 7.71 7.61 7.7
0.42 5.78 6.29 6.17 6.25
d d d d
Variable5 Variable6 Variable7 Variable8 Variable9
9.04 4.8 5.03 5.38 5.16
7.63 3.76 3.89 4.09 3.96
6.22 2.73 2.75 2.8 2.75
d d d d d
Variable10 Variable11 Variable12 Variable13 Variable14
4.21 4.51 3.17 3.32 3.46
3.08 3.4 1.92 2.05 2.09
1.96 2.3 0.665 0.779 0.707
d d d d d
Figure 9, 17 variables SOM with normalized inputs
Variable15 Variable16 Variable17
3.44 3.23 3.04
SOM model without input normalization showed final 2.07 1.96 1.8
quantitation error of 47.292. However, by the 0.711 0.693 0.559
normalization the inputs this quantization error is reduced d d d
SOM 24-Feb-2013
to 1.989. The final quantization error was: 1.989 and the
final topographic error was: 0.033. This shows that SOM Figure 11, Visualization of SOM U-Matrix and variables
analysis with normalized input variables provides far
accurate and reliable results as compared to the results Here in figure 11 above, matching the color code of each
without normalization. The first map in the figure 10 variable with U-matrix it can be seen that vertebral heights
below is the unified distance matrix or U-Matrix which L1, L2, L3, L4, L5 (corresponding to variables 1, 2, 3, 4, 5
represents overall behavior of the model. Variables 1 to 5 respectively) do not correlate with the age (dissimilarity
are the vertebral heights. Variable 6 to 11 are the disc with U-matrix). Disc heights T12-L1, L1-L2, L2-L3, L3-
heights and variable 12 to 17 are the disc signal intensities L4, L4-L5 and L5-S1 (corresponding to variables 6, 7, 8, 9,
of all 61 patients. The color of the units (neurons) in the 10, 11 respectively) show somewhat correlation with the
map shows the behavior of the specific neuron. Similar age. However, disc signal T12-L1, L1-L2, L2-L3, L3-L4,
color shows that the neurons are located close to one L4-L5 and L5-S1 (corresponding to variables 12, 13, 14,
another or similarity among the samples. 15, 16, 17 respectively) shows strong correlation with age.
VIII. Conclusion [12] Kohonen, Teuvo. "The self-organizing map."
Proceedings of the IEEE 78, no. 9 (1990): 1464-1480.
The objective of the SOM analysis was to observe [13] Vesanto, Juha, and Esa Alhoniemi. "Clustering of the
interrelationships that exist between 17 variables that were self-organizing map." IEEE Transactions on Neural
tested and thereby provides a basis for more advance Networks, 11, no. 3 (2000): 586-600.
analysis. The SOM does not replace existing statistical [14] Vesanto, Juha. "SOM-based data visualization
tools, but complements our ability to examine relationships methods." Intelligent data analysis 3, no. 2 (1999):
between disparate types of variables in a visual 111-126.
presentation of the data. By visualizing the SOM results [15] Vesanto, Juha, Johan Himberg, Esa Alhoniemi, and
obtained by normalized dataset, it was concluded that Juha Parhankangas. "Self-organizing map in Matlab:
lumbar spine vertebral height does not correlate with the the SOM toolbox." In Proceedings of the Matlab DSP
age whereas disc height shows somewhat correlation with Conference, vol. 99, pp. 16-17. 1999.
age. Disc signal intensities of lumbar spine show a strong [16] Ultsch, Alfred; Siemon, H. Peter (1990). "Kohonen's
correlation with the age. In future, other spinal features Self Organizing Feature Maps for Exploratory Data
will be incorporated to study the spinal aging process in Analysis". Proceedings of the International Neural
more depth. Network Conference (INNC-90), Paris, France, July
9–13, 1990. 1. Dordrecht, Netherlands: Kluwer. pp.
Acknowledgments 305–308. ISBN 978-0-7923-0831-7 (0-7923-0831-X).
[17] Ultsch, Alfred (2003); U*-Matrix: A tool to visualize
This project was partially supported by Warwick Impact clusters in high dimensional data, Department of
Fund, University of Warwick, United Kingdom. Authors Computer Science, University of Marburg, Technical
would like to thank the University Hospital Coventry and Report Nr. 36:1-12.
Warwickshire (UHCW) NHS Trust, Coventry, United [18] Ultsch, Alfred. "Maps for the visualization of high-
Kingdom for providing valuable data in the form of dimensional data spaces." In Proc. Workshop on Self
magnetic resonance images of the lumbar spine. organizing Maps, pp. 225-230. 2003.
[19] Vesanto, Juha, Johan Himberg, Esa Alhoniemi, and
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