Uncertainty of Measurement Results for Anatomical Structures of Paranasal Sinuses

Abstract

Medical specialists face a number of difficulties with processing of data obtained during spiral computed tomography (SCT). One of them is the objective selection of points for calculating the morphological characteristics of bone tissue.The goal of our study was to optimize interpretation of the data of radiological methods used for assessment of the paranasal sinuses with estimation of measurement uncertainty.

Full text

Medical specialists face a number of
difficulties with processing of data obtained
during spiral computed tomography (SCT).
One of them is the objective selection of points
for calculating the morphological
characteristics of bone tissue.The goal of our
study was to optimize interpretation of the data
of radiological methods used for assessment
of the paranasal sinuses with estimation of
measurement uncertainty
Uncertainty of Measurement Results for
Anatomical Structures of Paranasal Sinuses
Introduction
Theory/Approach/
Methodology
A total of 100 spiral computer tomograms (SCTs)
were studied; the CT scans were performed for
reasons not related to the disorders of Ear Nose and
Throat (ENT) organs.
The Hounsfield scale of this software showed the
density (max, min) of the upper and lower wall of the
maxillary and frontal sinus. Maximal and minimal
bone thickness also was calculated. In all sections,
visualizing the paranasal sinuses
All contributions of the uncertainties of the input
quantities form the standard uncertainty of the
measured quantity u(Hн) (the total standard
uncertainty uc, calculated according to the
dispersion summation rule.
The total standard measurement uncertainty of the
thickness of the walls of the paranasal sinuses Pн is
calculated using the following formula:
where uA(HHi) is the standard type A uncertainty,
uB(HHi) is the standard type B uncertainty, The
standard type A uncertainty is calculated using the
following formula:
where Hнi is the i-th value of sample measurement,
Hн is the mathematical expectation, n is the number
of measurements in a sample.
Standard type B uncertainty is calculated using the
following formula:
where σH is measurement error of the tool not
exceeding 0.0001%.
Contact: V. Alekseeva
vik13052130@i.ua
Results
References
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A.Nechyporenko, S.Krivenko, V.Alekseeva, A.Lupyr,
N.Yurevych, R.Nazaryan, V.Gargin
Kharkiv National University of Radio Electronics,
BioPromin LTD, Kharkiv National Medical University
The results of calculations of the total standard
measurement uncertainty of the thickness (UH) of the
lower wall of the maxillary and frontal sinuses are
presented in Table 1. The results of calculations of
the total standard measurement uncertainty of the
density (P) of the walls of the maxillary and frontal
sinuses are presented in Table 2. Then the interval
estimate of uncertainty is performed, namely, the
expanded uncertainty U according to the following
formula:
U=k ∙ uc (4)
where k is the coverage factor. The coverage factor
depends on the distribution law of the measured
value and the chosen level of confidence p. For these
samples, the hypothesis about the normal distribution
law is confirmed, therefore the coverage factor for the
probability of 0.95 is assumed to be 2.
Thus, the results of measurements taking into
account the expanded uncertainty U are given in the
tables 3, 4. Assessing the data in the table, we can
conclude that the probable spread of Y value is in the
±U range relative to the measured y value, and the
degree of certainty for Y values in this interval is
determined by the probability (confidence level) p =
0.95.
Name Thickness of the lower
wall of the maxillary
sinus
Thickness of the lower
wall of the frontal sinus
On the left On the
right
On the left On the
right
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
UH
(mm)
0.253
4201
3.641
9141
0.257
9491
1.2 2.869
5
1.721
7
1.238
6
2.110
5
TABLE I. TOTAL STANDARD MEASUREMENT UNCERTAINTY
OF THE THICKNESS OF THE LOWER WALL OF THE
MAXILLARY AND FRONTAL SINUSES
TABLE ΙΙ. TOTAL STANDARD MEASUREMENT
UNCERTAINTY OF THE DENSITY OF THE LOWER WALL OF
THE MAXILLARY AND FRONTAL SINUSES
Name Density of the lower wall
of the maxillary sinus
Density of the lower wall
of the frontal sinus
On the left On the
right
On the left On the
right
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Up
(mm)
220.1
78
306.7
461
197.6
17
310.2
026
155.2
82
374.2
4
138.2
17
366.1
371
TABLE ΙΙΙ. THE RESULTS OF MEASUREMENTS OF THE
THICKNESS OF THE LOWER WALL OF THE FRONTAL AND
MAXILLARY SINUSES, TAKING INTO ACCOUNT THE
EXPANDED UNCERTAINTY (Y=Y ± UEXTEND)
Name Thickness of the lower
wall of the maxillary
sinus
Thickness of the lower
wall of the frontal sinus
On the left On the
right
On the left On the
right
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Minim
um
Maxi
mum
Mini
mum
Maxi
mum
Uextend(
mm)
0.5068
40025 7.283
8282
0.515
8982
23
2.4 5.738
9
3.44
33
2.477
1
4.221
Y 1.4458
27815
±
0.5068
40025
9.9374
8344±
7.2838
282
0.8949
34211
±0.515
89822
3
2.17
±2.4
2.042
2±
5.738
9
4.37
49±
3.44
33
2.291
4±
2.447
7
4.054
5±
4.221
TABLE ΙV. THE RESULTS OF MEASUREMENTS OF THE
BONE DENSITY OF THE LOWER WALL OF THE FRONTAL
AND MAXILLARY SINUSES, TAKING INTO ACCOUNT
THE EXPANDED UNCERTAINTY (Y=Y ± UEXTEND)
Name Density of the lower wall
of the maxillary sinus
Density of the lower wall
of the frontal sinus
On the left On the
right
On the left On the
right
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Mini
mum
Maxi
mum
Uextend(
Hu)
440.3
56 613.4
882
395.0 620.
4051
310.5
6
748.
48
276.
43
732.
274
Y0.25
3420
1
3.641
9141
0.257
9491
1.2 2.869
5
1.72
17
1.23
86
2.11
05
To assess the quality of secondary processing of
tomographic images, it is advisable to introduce an
empirical criterion, which is based on estimation of
measurement uncertainty. The approach can be further
advanced and generalized for medical and technician
supports. We are not focusing on differentiation healthy
subjects from pathological one in current paper that could
be performed for estimation not only anatomical but
pathological peculiarities.
Fig.2. Visualization of the anatomical structures